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Although I haven't figured out all the clues, the final grid looks something like this, credit to Jacob Shetler, Remi Henry and M Oehm for solving some of the clues.

27. Sumerian city falls, ending Sufi celebration (3)

Aim = Bohemian reversed.

Here is the final grid (credit to Jacob Shetler, Remi Henry and M Oehm for solving some of the clues)

26. Retailers can cover the large and the small (5)

Lidls = Lid + L + S

27. Sumerian city falls, ending Sufi celebration (3)

Aim = Bohemian reversed.

59. No diaper, no happy couple (3)

Nay = a brand of baby clothes and also no + happy

Rua = aura backwards

Rua = aura backwards

48. Saudi Arabia owns any Chinese city (5)

Sanya = SanyA

Svalbard - Alba inside S.V.R & D

Lindblom - Lind + blo + M

Noomi - The end of Ban Ki-moon spelled backwards

Hypnosis - Hypervitaminosis without irate vim

Piano - Ethiopian opera

Uhura - heads up inside 'ura'

OSI - ISO backwards

Oar - sounds like ore

Uut - used underwater turtle

Queen

Bahamas - balsam? Ah, a beautiful

In situ - spins it up

Dumas - Duma is the lower chamber of the Russian parliament.

Singha - compounds in ghastly

Rua

AEG - Avenge

Ahab - Allahabad

Haar - ha(ng)ar

Eli - (R)eli(c) (figured out by M Oehm)

Ian - lesbian (credit to M Oehm)

Aim - Bohemian reversed.

AAA

Groom - living room

Uno - bonus

Ape - escapes

Vacuums - although vacua is usually the plural

Jordan

Toni - anagram of into

Sugar

Svalbard = Alba inside S.V.R & D

Lindblom = Lind + blo + M

Noomi = The end of Ban Ki-moon spelled backwards

Hypnosis = Hypervitaminosis without irate vim

Piano = Ethiopian opera

Uhura = heads up inside 'ura'

OSI = ISO backwards

Oar = sounds like ore

Uut = used underwater turtle

Queen = Queue - U(-turn) + next (thanks M Oehm)

Bahamas = balsam? Ah, a beautiful

In situ = spins it up

Dumas = Duma is the lower chamber of the Russian parliament.

Singha = compounds in ghastly

Rua = aura backwards

AEG = Avenge

Ahab = Allahabad

Haar = ha(ng)ar

Eli = (R)eli(c) (figured out by M Oehm)

Ian = lesbian (credit to M Oehm)

Aim = Bohemian reversed.

AAA = both an American motor club and bond credit rating

Groom = living room

Uno = bonus

Ape = escapes

Vacuums = although vacua is usually the plural

Jordan = Michael Jordan (basketballer) or Jordan (Katie Price)

Toni = anagram of into

Sugar = meaning to sweeten and is synonymous with honey as an informal address.