Across:
8 Part of the theorem overcompensates (part of the ‘theoREM OVErcompensates’ = REMOVE) for shift (REMOVE),
9 The subtle insinuation (INNUENDO) from union (union) movement (= anagram indicator) (union = INNU-O) accommodating wind-up (-END-) (INNUENDO)
10 Look out for (SEEK) follower of Punjabi guru (Sikh) speaking (= homophone indicator) (‘Sikh’ = ‘SEEK’),
11 Consult the Oracle (SEEK ADVICE) in 10 across (‘seek’ = SEEK) for Bill (AD-) and gutless (n) Vince (gutless ‘vince’ without ‘n’ = -VICE) (SEEK ADVICE),
12 Open bar (open ‘Bar’ = B-) to begin with (first = 1ST = -IST-) for most of (d) staff (staff/stock = ‘rod’ without ‘d’ = -RO) (BISTRO) in small restaurant (BISTRO),
14 Sounds like (= homophone indicator) a few Hail Marys and Our Fathers (‘penance’ = ‘PENNANTS’) for flying the flag for crafty James Joyce and Samuel Beckett? (flying the flag for LÉ James Joyce and LÉ Samuel Beckett = PENNANTS / flags on ship),
15 4 down (‘time’ = TIME) is from old (O-) New York (NY = -N Y) and belongs to US? (belongs to us / -OUR) 24 down (‘hand’ = HAND-) is from heart of Essex (heart of ‘esSex’ = -S) (TIME ON YOUR HANDS) and is not busy! (TIME ON YOUR HANDS),
18 Skilful type (VIRTUOSO) is against (versus = V-) riotous (riotous) change (= anagram indicator) (riotous = -IRTUOSO) (VIRTUOSO),
20 Coming around (WAKING) to Washington (WA-) head of state (-KING) (WAKING),
22 Taking great care (DILIGENTLY) of Diana (DI-) and Elizabeth (LI-LY) Ring? A man of some refinement! (-GENT-) (DILIGENTLY),
24 Headmistress ignores disaster (‘headmistress’ ignores ‘disaster’ = hems = HEMS) of the frills from sewing class (HEMS),
25 Frank (STRAIGHT) Blunt? (STRAIGHT),
26 Most of (e) the view (‘see’ without ‘e’ = SE-) on river (-NILE) (SENILE) is declining as the years go by (SENILE).
Down:
1 Sporting (= anagram indicator) enemy (enemy = YEMEN-) is one (-I) (YEMENI) living in Arabian peninsula (YEMENI),
2 Weird leaving fieldwork (‘weird’ leaving ‘fieldwork’ = flok = FOLK) to the ordinary people (FOLK),
3 Shatters the illusions of (LETS DOWN) accommodations (LETS) in Northern Ireland (Co DOWN) (LETS DOWN),
4 What one behind bars called (what one behind bars/barman called = TIME) the fourth dimension (TIME),
5 Tito leaves invitation (‘Tito’ leaves ‘invitation’ = invain = IN VAIN) to no avail (IN VAIN),
6 Create an impression of late (LEAVE A MARK) with work in tattoo parlour (LEAVE A MARK),
7 Knowledgeable (EDUCATED) Oriental (East = E-) theologian (doctor of divinity = -D-D) getting to grips with acute (acute) problem (= anagram indicator) (acute = -UCATE-) (EDUCATED),
13 Stage (THEATRICAL) of decomposed (= anagram indicator) cattle hair (cattle hair = THEATRICAL),
14 Osteopath loses seat (‘osteopath’ loses ‘seat’ = otoph = PHOTO) and it’s captured for posterity by the cameraman (PHOTO),
16 Titian (Titian = -NITIAT-) confused (= anagram indicator) in Ireland (Ireland domain = .ie = I-E) (INITIATE) with new member (INITIATE),
17 My word is (my word is) distorted (= anagram indicator) (my word is = ROWDYISM) by noisy and disorderly behaviour (ROWDYISM),
19 Turns up (= reverse indicator), for example (e.g. = -GE), to study (den = -N ED-) at Oxford (O-) (ON EDGE) a bundle of nerves (ON EDGE),
21 Graceful on the ground (NIMBLE) with heads of mulberry bushes (heads of ‘Mulberry Bushes’ = -MB-) in flower (flower/river = NI-LE) (NIMBLE),
23 At all costs dismiss call as (‘at all costs’ dismiss ‘call as’ = tost = TOTS) coming from youngsters (TOTS),
24 Hook (HAND) and Sutherland fail to get result (‘Sutherland’ fail to get ‘result’ = hand = HAND).