Across:
1 Accepted a mate, joining the institute that is United, (got married / TOOK THE PLUNGE) dived (TOOK THE PLUNGE),
10 No top (p) for opening (‘pore’ without ‘p’ = ORE-) pack (gang) reduced (g) (‘gang’ without ‘g’ = -GAN-) with old (-O) (OREGANO) herb (OREGANO),
11 Showing off (BRAVADO) daring (brave) clip (e) (‘brave’ without ‘e’ = BRAV-) from a (-A-) party (-DO) (BRAVADO),
12 Knowhow to start (‘Knowhow’ to start = K-) to fish (-EEL) (KEEL) in part of ship (KEEL),
13 Shirley said (= homophone indicator) (‘Shirley’ = ‘surely’) take the last goodie (last ‘goodiE’ = ‘e’) away (‘surely’ without ‘e’ = SURLY) from one who’s bad-tempered (SURLY),
15 Selected (TOOK) on all sides today (TOOK on all sides of today’s grid),
17 Foot the bill for (PAY) raising (= reversal indicator) containment of Barbary apes (containment of ‘BarbarY APes’ = yap = PAY),
19 Fires (INGLES) court figures (tennis court ‘singles’) starting off (s) (‘singles’ without ‘s’ = INGLES),
21 Let go a (let go a = LEGATO) hammer (= anagram indicator) smoothly (LEGATO),
22 It (-IT-) is found in sun block (visor = VIS-OR) (VISITOR) although it’s alien to some of us (alien / VISITOR),
23 A fair amount of (half of) fat (half of ‘LArd’ = -LA-) in flipping (= reversal indicator) rice (rice = EC-IR) (ECLAIR) cake (ECLAIR),
25 Hook (BUTTON) by Ultimate Heavyweight (ultimate ‘heavyweighT’ = -T-) in bout (bout = BUT-O-) grounds (= anagram indicator) leading newcomer (leading ‘Newcomer’ = -N) (BUTTON),
27 Local American address (MAC) in Oklahoma City (in ‘oklahoMA City’ = MAC),
29 Those around the borders to come home (those around the borders ‘TO come hoME’ = TOME) for the publication (TOME),
30 Part of the family (S-ON) includes a (-A-) line (-L-) (SALON) from a large house (SALON),
31 One (I-) raised (= reversal indicator) in 20 down (‘sir’ = -RIS) (IRIS) and in the flowerbed (IRIS),
34 Have a liking for (ENAMOUR) a menu or (a menu or = ENAMOUR) treat (= anagram indicator),
35 The price of confession (PENANCE) produced by coppers (pence = PEN-CE) arresting fellow (man) blowing his top (m) (‘man’ without ‘m’ = -AN-) (PENANCE),
36 What someone with gripe did (TOOK EXCEPTION) to withdraw (TOOK) from special case (EXCEPTION) (TOOK EXCEPTION).
Down:
2 Ludicrously embellish (OVER-EGG) for Shell? (OVER-EGG),
3 Upsetting (= reversal indicator) in Louisiana, Oklahoma? (in ‘LouisiaNA, OKlahoma’ = naok = KOAN) That’s a riddle you won’t work out! (paradoxical riddle without a solution = KOAN),
4 Get together (HOOK UP) for clip of pugilist (HOOK) taking the head off (p) boxer (‘pup’ without ‘ p’ = UP) (HOOK UP),
5 Little Rock’s description (little rocks description = PEBBLY) of park (P-) with accommodation (B&B = -BB-) in place in Dublin (Ely Place = -E-LY) (PEBBLY),
6 The state of the beehive (The Beehive State = UTAH) and rose from Art House (‘rose’ from ‘Art House’ = athu = UTAH),
7 Recipe (-R-) in Angola? (Angola = G-ANOLA) Bananas (= anagram indicator) (GRANOLA) served up for breakfast! (GRANOLA),
8 Seized part of Dublin (TOOK LIBERTIES) and showed no respect (TOOK LIBERTIES),
9 Retired (TOOK TO ONE’S BED) – presumably, this is what the gardener with the nightshade did? (TOOK TO ONE’S BED),
14 Endless (o) wireless (‘radio’ without ‘o’ = RADI-) communications initially (‘Communications’ initially = -C-) on a (-A-) line (-L) (RADICAL) that’s a revolutionary type (RADICAL),
16 Resided (lived = DEVIL) over (= reversal indicator) with underworld boss? (DEVIL),
18 Some (‘some’ = ‘sum’ = S-UM) State (= homophone indicator) welcomes Queen (Elizabetha Regina = -ER-) (SERUM) providing immunity for the royal blood presumably (SERUM),
20 Educationalist (SIR) retires (= reversal indicator) in impoverishment (in ‘impoveRIShment’ = ris = SIR),
21 Sample of Buffalo Bill’s (sample of ‘BuffaLO Bills’ = LOB) pelt (pelt/fling = LOB),
24 New (= anagram indicator) album (album = LUMBA-) by legend (‘leG’ end = -G-) is over-the-top (‘Over’ the top = -O) (LUMBAGO) and a pain in the rear (LUMBAGO),
26 Fatty part of the tuna (TORO-) is not (not = -NTO) cooked (= anagram indicator) (TORONTO) in Canada (TORONTO),
27 Listens in coming out of Marxist-Leninist (‘listens in’ coming out of ‘Marxist-Leninist’ = marxit = MATRIX) Square one associates with mathematician (MATRIX),
28 Run (-R-) into State (= homophone indicator) Police (‘cops’ = ‘copse’ = CO-PSE) (CORPSE) in the dead centre of the hospital (CORPSE),
32 Storms out of stockrooms (‘storms’ out of ‘stockrooms’ = ckoo = COOK) and out of the kitchen (COOK),
33 Leo is no longer in the lineout (‘Leo’ is no longer in the ‘lineout’ = inut = UNIT) for company (UNIT).