Across:
1 Starts to acclimatise (starts ‘to acclimatise’ = -TA-) in top-class (posh = PO-SH) (POTASH) agricultural compound (POTASH),
4 Siege can (siege can = AGENCIES) damage (= anagram indicator) the levers of American government (AGENCIES),
9 Academic (learned) lost the head (l) (‘learned’ without ‘l’ = EARNED) and got what he deserved, financially speaking (EARNED),
10 Bachelor (BA = AB-) backs (= reversal indicator) topless (c) bathing area (‘cove’ without ‘c’ = -OVE) for everyone (ALL) (ABOVE ALL) in a heavenly location (ABOVE ALL),
12 Whatever you say, say nothing (STONEWALL) to Pip (pip = STONE-) at barrier (-WALL) (STONEWALL),
13 Pick off tipsy cake (‘pick’ off ‘tipsy cake’ = tsyae = YEAST) one of the ingredients for breadmaking (YEAST),
14 Management directives perhaps to man of letters (POSTAL ORDERS) employed in the past by those transferring money (POSTAL ORDERS),
18 Flower (flower/river = PO-) section (-STAGE) is to impress (STAMP) (POSTAGE STAMP), for example, one of the Hawaiian Missionaries, (one of the ‘Hawaiian Missionaries’= POSTAGE STAMP),
21 Learn to fit in (ADAPT) data (data = ADA-T) collected (= anagram indicator) around park (-P-) (ADAPT),
22 English (E-) jokers (jokers = -C-OMICS) welcoming switch (-ON-) (ECONOMICS) to the study of the development of capital (ECONOMICS),
24 Oscar (O-) and Vera (-VER-A-) admit drawing attention (-LO-) to director (-D) (OVERLOAD) of Swamp (swamp/burden = OVERLOAD),
25 Learnt (learnt = RENTAL) builder (= anagram indicator) provided temporary accommodation (RENTAL),
26 Drop a line (FISH) to sweet thing (CAKE) (FISH CAKE) – a dishy type in the seafood restaurant (FISH CAKE),
27 Icelanders drop line (‘Icelanders’ drop ‘line’ = ceadrs = CADRES) to small military groups (CADRES).
Down:
1 Exercises (PRESS-UPS) little dogs (P-UPS) burying most of (c) the salad stuff (‘cress‘ without ‘c’ = -RESS) (PRESS-UPS),
2 Tories to (Tories to = TORTOISE) worry (= anagram indicator) one of those enjoying a slower pace of life (TORTOISE),
3 Song and dance (SCENE) witnessed in the abbey (SCENE in The Abbey Theatre),
5 Local mouthy type (GOB-) showed the way (-LED-), for example (e.g. = -EG-), in novel (-B-OOK) (GOBBLEDEGOOK) with obscure language (GOBBLEDEGOOK),
6 Those laying the foundations for future task forces (NAVY YARDS) providing work for craft workers (NAVY YARDS),
7 Having trouble (IN A JAM) with James the First (‘James’ the first = J-) over crazy (= anagram indicator) mania (mania = IN A -AM) (IN A JAM),
8 Take one’s hat off (SALUTE) as a gesture to the company (a gesture to the company/soldiers = SALUTE),
11 Put the wind up the little fellow perhaps (break wind = PAT ON THE BACK) with bit of encouraging praise? (PAT ON THE BACK),
15 A co-pilot’s (a co-pilots = APOSTOLIC) mistake (= anagram indicator) concerns father in Rome (APOSTOLIC),
16 Outlaw (BAN-) loses the head (s) with relative (‘sister’ without ‘s’= -ISTER) (BANISTER) for offering protection to one of those taking flight? (BANISTER),
17 Presumably, sent by a man of letters (EPISTLES) to run (= anagram indicator), sit, sleep (sit sleep = EPISTLES),
19 Left (l) out of deciding game (‘play off‘ without ‘l’ = PAY OFF) as a bribe (PAY-OFF),
20 Included in Vespa personalised (included in ‘Vespa personalised’ = PAPERS) for archivist going to work (PAPERS),
23 Upsets (= reversal indicator) American (-A) agent (rep = -PER-) linked to fair amount of (half of) (half of ‘of’ = O-) (OPERA) musical drama (OPERA).