Did Gondor ever reach the previous height of its power during the Fourth Age?

Question

As far as I know the peak of Gondor's glory during the rule of the House of Anarion was during the reign of Hyrarmendacil I; the kingdom extended to most of ME, including Greenwood the Great, Rhun, Harad and Rohan. It is stated that Aragorn conquered most of these lands:

Aragorn led the forces of the Reunited Kingdom on military campaigns against some Easterlings and Haradrim, re-establishing rule over much territory that Gondor had lost in previous centuries.

And also laid Mordor under his dominion. But did the Reunited Kingdom extend more geographically and hold more power than during the days of the kings of previous years?

Answer 1

We don't know

Tolkien never wrote much about the Fourth Age, however he had begun a sequel to tLotR titled The New Shadow. Unfortunately Tolkien did not like the direction is was headed in and abandoned it after only 13 pages.

I did begin a story placed about 100 years after the Downfall [of Mordor], but it proved both sinister and depressing. Since we are dealing with Men it is inevitable that we should be concerned with the most regrettable feature of their nature: their quick satiety with good. So that the people of Gondor in times of peace, justice and prosperity, would become discontented and restless – while the dynasts descended from Aragorn would become just kings and governors – like Denethor or worse. I found that even so early there was an outcrop of revolutionary plots, about a centre of secret Satanistic religion; while Gondorian boys were playing at being Orcs and going round doing damage. I could have written a 'thriller' about the plot and its discovery and overthrow – but it would be just that. Not worth doing.
_{The Letters of J.R.R. Tolkien, Letter 256 - 13 May 1964}

I couldn't find any mention of the extent of Aragorn's lands, or the quote you provided in the Letters of J.R.R. Tolkien

Finally, 15 months before his death, Tolkien wrote a letter to Douglas Carter, informing him of what he'd written about the Fourth Age

I have written nothing beyond the first few years of the Fourth Age. (Except the beginning of a tale supposed to refer to the end of the reign of Eldaron about 100 years after the death of Aragorn. Then I of course discovered that the King's Peace would contain no tales worth recounting; and his wars would have little interest after the overthrow of Sauron; but that almost certainly a restlessness would appear about then, owing to the (it seems) inevitable boredom of Men with the good: there would be secret societies practising dark cults, and 'orc-cults' among adolescents.)
_{The Letters of J.R.R. Tolkien, Letter 338 - 6[?] June 1972}

Answer 2

Tolkien provides the following description of the boundaries of Gondor following Hyarmendacil's victory over the Men of Harad in TA 1050.

The might of Hyarmendacil no enemy dared to contest during the remainder of his long reign. He was king for one hundred and thirty-four years, the longest reign but one of all the Line of Anárion. In his day Gondor reached the summit of its power. The realm then extended north to the field of Celebrant and the southern eaves of Mirkwood; west to the Greyflood; east to the inland Sea of Rhûn; south to the River Harnen, and thence along the coast to the peninsula and haven of Umbar. The Men of the Vales of Anduin acknowledged its authority; and the kings of the Harad did homage to Gondor, and their sons lived as hostages in the court of its King. Mordor was desolate, but was watched over by great fortresses that guarded the passes.

_{The Lord of the Rings Appendix A, Section 1: The Númenórean Kings
Page 1045 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)}

Arnor

One significant part of the Reunited Kingdom that was not part of Gondor at its height is, of course, Arnor. It is the inclusion of Arnor that makes Aragorn's land the Reunited Kingdom.

Arnor presumably includes at least all the land it did at its height, which Tolkien describes as:

‘Eriador was of old the name of all the lands between the Misty Mountains and the Blue; in the South it was bounded by the Greyflood and the Glanduin that flows into it above Tharbad.

‘At its greatest Arnor included all Eriador, except the regions beyond the Lune, and the lands east of Greyflood and Loudwater, in which lay Rivendell and Hollin.

_{The Lord of the Rings Appendix A, Section 1: The Númenórean Kings
Page 1039 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)}

As Hollin (Eregion) is now deserted, there is probably no reason for it to be excluded from Arnor, and the same may apply to Rivendell and Lindon once the elves leave.

The Shire

The Shire has been self-governing for centuries, but was still considered part of Arnor and is part of the Reunited Kingdom.

At the end of the Third Age the part played by the Hobbits in the great events that led to the inclusion of the Shire in the Reunited Kingdom awakened among them a more widespread interest in their own history; and many of their traditions, up to that time still mainly oral, were collected and written down.

_{The Lord of the Rings Prologue: Note on the Shire Records
Page 14 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)}

Rohan

Rohan (formerly Calenardhon) was part of Hyarmendacil's Gondor but is not part of the Reunited Kingdom. Cirion the Steward of Gondor gave Calenardhon to Eorl and his descendants until the King returns. When he becomes King, Aragorn confirms the gift.

In Gondor the King Elessar now ruled, and in Arnor also. In all the lands of those realms of old he was king, save in Rohan only; for he renewed to Éomer the gift of Cirion, and Éomer took again the Oath of Eorl.

_{The Lord of the Rings Appendix A, Section 2: The House of Eorl
Page 1071 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)}

The Forest of Drúadan

The Forest of Drúadan is located in Anórien and so was part of Gondor. On his way to Théoden's funeral, Aragorn gives it to Ghân-buri-Ghân. It is, of course, possible that this should be interpreted as creating another self-governing enclave within the Reunited Kingdom (like the Shire), but I like to think that "to be their own" should be taken literally.

Without haste and at peace they passed into Anórien, and they came to the Grey Wood under Amon Dîn; and there they heard a sound as of drums beating in the hills, though no living thing could be seen. Then Aragorn let the trumpets be blown; and heralds cried:

‘Behold, the King Elessar is come! The Forest of Drúadan he gives to Ghân-buri-Ghân and to his folk, to be their own for ever; and hereafter let no man enter it without their leave!’

Then the drums rolled loudly, and were silent.

_{The Lord of the Rings Book Six, Chapter 6: Many Partings
Page 976 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)}

Mordor

At the start of the Third Age, Gondor controlled Mordor. As far as we know, they didn't settle there (apart from staffing the forts that guarded its borders). It was not until after the time of Hyarmendacil that Sauron's forces reoccupied Mordor.

At the end of the Third Age, Mordor is again defeated and I assume is considered part of the Reunited Kingdom. Aragorn give the only fertile part of Mordor to Sauron's former slaves.

And the King pardoned the Easterlings that had given themselves up, and sent them away free, and he made peace with the peoples of Harad; and the slaves of Mordor he released and gave to them all the lands about Lake Núrnen to be their own.

_{The Lord of the Rings Book Six, Chapter 5: The Steward and the King
Page 968 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)}

East Lórien

Hyarmendacil's Gondor "extended north to the field of Celebrant and the southern eaves of Mirkwood". It is likely that at the end of the Third Age, the southern eaves of Mirkwood became part of the new Elvish land of East Lórien (at least until the elves departed).

In the North also there had been war and evil. The realm of Thranduil was invaded, and there was long battle under the trees and great ruin of fire; but in the end Thranduil had the victory. And on the day of the New Year of the Elves, Celeborn and Thranduil met in the midst of the forest; and they renamed Mirkwood Eryn Lasgalen, The Wood of Greenleaves. Thranduil took all the northern region as far as the mountains that rise in the forest for his realm; and Celeborn took all the southern wood below the Narrows, and named it East Lórien; all the wide forest between was given to the Beornings and the Woodmen.

_{The Lord of the Rings Appendix B, Section 2: The Third Age
Page 1094 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)}