Across:
1 Bride hung out rug (‘bride hung’ out ‘rug’ = bidehn = BEHIND) out the back (BEHIND),
4 Initially slimmer (initially ‘slimmer’ = S-) and fitter (-TRIMMER) (STRIMMER) from cutting down on the grass (STRIMMER),
9 There’s no way out after this (CURFEW) old police force (RUC = CUR-) retires (= reversal indicator) a relatively small handful (-FEW) (CURFEW),
10 Bishop (B-) Alan (-ALAN-) Clare (-CE-), head of school, (head of school = -S) (BALANCES) settles accounts (BALANCES),
12 Sends in a curriculum vitae (applies = APPL- -IES) including record (extended-play record = EP = -E P-) (APPLE PIES) – the typical Americana stuff (APPLE PIES),
13 Detective (-PI-) in France where (French ‘where’ = O-U-) Frenchman (Monsieur = -M) (OPIUM) produced drug (OPIUM),
14 Top man (ALPHA- male) back (-BET-) in charge (in charge = -IC-) with gangster (Al Capone = -AL) (ALPHABETICAL) produces a type of order (ALPHABETICAL order),
18 Something for the cyclist (CHAIN-) lighting up (-SMOKING) (CHAIN-SMOKING) by taking drugs one after another perhaps (CHAIN-SMOKING),
21 Some Bengali enterprise (some ‘Bengali enterprise’ = ALIEN) is unfamiliar (ALIEN),
22 Stepping out (HOOFING IT) by doing something for 2 down (HOOFING IT for ‘hornpipe’),
24 Brief (e) project (project/jut out = ‘bulge’ without ‘b’ = BULG-) performed for opera (-ARIA) (BULGARIA) in Eastern Europe (BULGARIA),
25 Loose (ADRIFT) billboard (AD-) for Split (split/crack = -RIFT) (ADRIFT),
26 Ruby (RED-) gets engineer (-E-) to stop (stop -SIGN) (REDESIGN) new plan (REDESIGN),
27 Spin out (EXTEND) part in next Endeavour (part in ‘next Endeavour’ = EXTEND).
Down:
1 Bet (BACK) on a (A-) course (-WAY) (BACK AWAY), as to how one might take flight (BACK AWAY),
2 Noisy type in car (HORN-) takes channel (-PIPE) (HORNPIPE) for overseas dance (HORNPIPE dance for sailors),
3 Sample of brownie certified (sample of ‘brownie certified’ = NIECE) by relative (NIECE),
5 Broadcast (TRANSMISSION) in part relates to petrol heads (car TRANSMISSION),
6 Boyfriend (INAMORATO) reviews all (= reverse all indicator) good books (Old Testament = OT = -TO) from key (music key -A-) Italian (Roman = -NAMOR-) institute (I-) (INAMORATO),
7 Help out (MUCK IN) presenter (emcee = MC = M-C-) welcoming Ulster (-U-) family (kin = -K IN) (MUCK IN),
8 Coal pits out of precious metals (‘coal pits’ out of ‘precious metals’ = reusme = RéSUMé), in summary? (RéSUMé),
11 Going to blazes (FIREFIGHTING) to show someone the door (sack / FIRE-) for violent behaviour (-FIGHTING) (FIREFIGHTING),
15 Anna is the (Anna is the = ATHENIANS) criminal (= anagram indicator) living in Greece (ATHENIANS),
16 One of the calls (RING-) by Munster (-SIDE) (RINGSIDE) leads to a fight in the middle of arena (RINGSIDE),
17 A (A-) soldier (-GI-) from leaderless (s) country (‘state’ without ‘s’ = -TATE-) finds diamonds (-D) (AGITATED) and gets jittery (AGITATED),
19 Is capable of giving a clip around the ears (BARBER) for hurtful remark (BARB-) in hospital (-ER) (BARBER),
20 Ill-treated without Earl (‘ill-treated’ without ‘Earl’ = iltted = TITLED) – the noble one (TITLED),
23 Laid off in Dixieland (“laid” off in “Dixieland” = ixend = INDEX) from the book section (INDEX).