I would say that we just don't know who this ruler is. However, it could be Baldr. You have to remember here that Baldr is actually a fairly important member of the Aesir. He is often forgotten because Odin and Thor are so popular but, after all, the Gylfaginning says of Baldr "He is best, and good things are to be said of him". Obviously, Baldr dies before Ragnarök. However, the return of Baldr after Ragnarök is attested to in stanza 62 of the Völuspá:
"Baldr man koma; búa þeir Höðr ok Baldr Hropts sigtoptir vel valtívar."
"Baldr shall come; Höðr and Baldr will live in Odin's great war hall of the slain gods"
That's my own translation from the Old Norse and it makes me think that there's a possibility Baldr could be the mighty ruler you're looking for. However, this is the only source which states Baldr will return after Ragnarök, the others say that Viðar and Váli are the only survivors. Norse mythology is often abstract. It could be that the stanza above from Hyndluljóð isimplying that Baldr is this "mightier" ruler.
Or on the other hand, it could be that we just don't know that far into Norse cosmology because "Few are able to see beyond The moment that Óðinn shall meet the Wolf". Either way, it's an interesting point and I'd like to hear some other views on the matter.
John Grant, in An Introduction to Viking Mythology, says that "Christianity made its mark on Norse mythology, too, and it is recorded that, after Ragnarok, there will be the incarnation of a god too great to be named - in other words, Jahweh." Presumably he's referring to our lines from Hyndluljóð. All the books I've read on Norse mythology which mention those lines from the poem seem to agree in identifying this unnameable one with Jesus Christ. The idea is that the Christian compilers of the old stories from the mythology interpolated that section of this poem so that it subtly alluded to Christ. That sounds about right (to me anyway), since there doesn't seem to be much reason for Hyndla to so greatly fear naming Balder or any of the other old gods, who elsewhere are mentioned with no such reservation.
I'm not disagreeing with you. But it's interesting you should say that because Odin says of Höðr in part XXII of the Gylfaginning "the gods would desire that no occasion should rise of naming this god" and it just so happens that Höðr is one of the four gods who is alive after Ragnarök.
I've no problem with disagreement, since it keeps discussion(s) going ! I guess I've never thought of Höðr in that way for two reasons.
One is the immediately preceding description of the dude in the same line of the Gylfaginning that you've quoted, where Óðinn says first that he is blind and then "He is of sufficient strength". That almost conciliatory picture of this god seems quite difficult to reconcile with Hyndla's unnameable future ruler, who is "mightier than he" or, according to a different translation, one who is "greater than all". That is of course not to say that there is no way that Höðr could eventually somehow have become mightier than his father or greater than all, but as it stands he just doesn't seem to fit that bill. His twin Balder would be much better suited to this, considering the glowing reviews he receives from everyone in the mythology who speaks of him (Loki [& the giantess Þökk who we suppose must've been Loki in disguise] being the glaring exception, of course). Viðarr and Váli, in fact, minor characters as they may be, from their father's description of them in the Gylfaginning, are so much mightier than Höðr.
The other reason is that Óðinn does not seem to be expressing fear of naming Höðr in the Gylfaginning, rather he's just telling Gylfi that the Æsir would much prefer not to talk about the guy who killed the best and most loved one among them all, despite Loki having borne the motive for this demise. But the thing is that, in giving Gylfi this information, Óðinn does name the undesirable god and talk about him, albeit ever so briefly, as opposed to Hyndla who quickly glides over her vague description of her mighty one who is yet to come. But having said all that, Höðr is an important component of the chain reaction of events leading up to the Ragnarök, what with Balder's death at his hand being the primary catalyst (or precursor), after Balder's nightmares, of the final cataclysm in which lies the doom of the gods.
(late in this thread, but whatever) One theory I have is that it might well be jesus, or maybe even the english word "god" that it was referring to. But that doesn't mean that the Norse gods are fake, or that jesus and all is the real god. The things that predominantly shows up in almost every religion/culture/worship of any deity is; Sacrifice, praise and all together giving of energy to the entity.
Which makes sense because one of the laws of the universe is that everything comes from consciousness, every atom controlled by thought. But with the perfect design of today we have so many things buzzing around in our head that our thoughts mean jack all, and really the only time most people of today take to focus their thoughts is either on bad **** they don't want to happen (more of a catalyst than anything) or praying to jesus. So to me it makes sense that she didn't name him, because in naming him the thought pops up into our mind and in essence we are feeding this new deity as we deprive the Norse deities.
It's like if you lived on a planet of lower beings and the only way not to starve was for them to worship you. but you're selling honor and virtues, while a group of lower beings have fabricated their own higher being and are spreading fear by saying anyone who doesn't follow their god will be stuck in a place of pain and suffering in which they die repeatedly forever (which sounds more like not learning your lesson for subsequent incarnations). and then they actually tell their followers that your followers are evil witches and mindless barbarians (I don't even want to explain how that turned out).
But basically what I was trying to say was; This entity is getting a lot more power given to it than odin had, thanks to the current cultural center of the world clinging to him and all the christian stuff that floats about on tv and the internet. Odin had many followers, but not as many as this. I mean possibly, in the last existence. But I suppose we'll never know for certain. (I'm not trying to spam post, I just have a bad habit of thinking about vital things after posting)
I have a real problem with any sort of philosophy that the gods or goddesses in old religions somehow needed the good thoughts/prayers/belief/sacrifices of people to be powerful or to thrive. That's just silly to me, and a lot of times it goes contrary to the myths of the ancient religion in question.
I see the gathering in Ithavoll/Iðavöllr as a peaceful gathering after the world has known war, and very long winter, and fire - of "Of the terrible girdler | of earth they talk" I think not as only Jörmungandr - but the threat at the end of Völuspá, of the coming rising of Níðhöggr. I do not think it a thing that happens during Ragnarök.
"Baldr and Hoth dwell | in Hropt's battle-hall" Hropt is Sage, or Odin. Hoth is another name for Höðr. It's interesting that in this time of peace and beauty there is again need for a battle-hall in Asgard or Ithavoll.
Hönir is mentioned to winning a prophetic wand, he is identified with Vili "will" the brother of Odin, he went to the Vanir as a hostage with Mímir (As Njörðr and Freyr for Hönir; Kvasir for Mimir - the last two both die, Mimir's beheaded although it is a head which Odin talks to, and Kvasir is drained of blood by Fjalar and Galar and it's mixed with honey making the mead of poetry put in two vats Són and Boðn, and a pot called Óðrerir) of the gifts when given to Ask and Embla by Odin, Lóðurr and Hönir, he gave them reason (Lóðurr identified with Loki and Vé).
"And the sons of the brothers | of Tveggi abide
In Vindheim now: | would you know yet more?"
Tveggi being Odin, so it seems to say the sons of Hönir/Vili and Loki/Vé are alive. And if not allies, close by.
Víðarr, the son of Odin and Gríðr who avenges his father's death by Gram/Fenrir, personally I see Fenrir not as Garm, and think Garm a name for Loki's other son by Sigyn who is changed into a wolf and kills his brother (his brother's guts are used to keep Loki tied) being named Váli and Nari or Narfi; it's interesting the name Váli son of Loki and Sigyn and the other Váli the son of Odin and Rindr born to avenge Baldr's death by killing his brother Höðr.
I think Loki was thought to be tied to three stones under a grove of hot springs, perhaps these were meant to be the wells - Urðarbrunnr, Hvergelmir, and Mímisbrunnr; that being he was tied to the Yggdrasil and likely the Ginnungagap. Perhaps the snake with it's dripping venom was Níðhöggr. It would explain how he was both a god of fire and how his shaking made earthquakes. I would likely have tied it all to Ymir again, with Narfi or Nörfi/Nörr somehow reviving to produce Nótt, the night. I think of Ginnungagap as having no time, where ending and beginning is a thing of Niflheim and Muspelheim. It's clear enough that the Norse gods don't seem to worry about dying, at least in the case of Baldr and Mimir and Kvasir - dying isn't the end, and certainly the warriors picked by Freyja and Odin expected to live to fight another day.
Which brings to mind the question of what happened to Freyja who is not mentioned as dying in Ragnarök her Fólkvangr where her first choice of warriors that fell in battle are, and her hall Sessrúmnir - what of it? Are they supposed to be who (with Líf and Lífþrasir) bring about human kind again?
In any case, Thor's sons Móði and Magni (who share Mjollnir after Thor falls) join the others in Iðavöllr or Gimli - of all of them, I think that Magni (the "mighty") would be ruler.
Not only does he have a share of Mjollnir but when the giant Hrungnir on Gullfaxi chased Odin and Sleipnir to the gates of Asgard, it was only by a invitation to drink there that might have saved Odin's head because he had boasted Sleipnir the better horse but Hrungnir would have proven Odin wrong if he had caught him for Gullfaxi was the longer lasting and could like Sleipnir run on land, in the air, and on the sea. Gullfaxi was given to Magni by Thor - not Odin, and at this Odin was upset, but Thor thought to reward his son who at three days old was the only one (after Thjalfi and the combined strength of the Aesir fail) able to lift the limb of Hrungnir which trapped Thor. Magni was half giant the son of Járnsaxa (potentially one of the nine mothers of Heimdallr who was a forefather of a system of social castes among mankind) in the Skáldskaparmál.