Across:
1 Half suppressed laugh (TITTER) from Troy (T-) getting beer (bitter) with no head (‘bitter’ without ‘b’ = -ITTER) (TITTER).
4 Faith (IDEOLOGY) gets papers (ID- papers) from Spain (-E-) to go with a fair amount of (half of) technology (half of ‘technOLOGY’ = -OLOGY) (IDEOLOGY),
9 Sailor (-TAR-) has time (-T-) in boat (S-S) (STARTS) for the new jobs (STARTS),
10 Gave the go ahead (ASSENTED) to a (A-) society (-S-) with Cologne (scent) speech (= homophone indicator) (‘scent’ = ‘sent’ = -SENT-) writer (-ED) (ASSENTED),
12 Attract attention of CAB (CALL A TAXI) accountant (C- A) over everything (-ALL) to do with compulsory contribution to Revenue (TAX-) unit (-I) (CALL A TAXI),
13 Nutcase (SKULL) in West Cork (Schull) report (= homophone indicator) (‘Schull’ = ‘SKULL’),
14 One of those taking out a lot of people (SERIAL KILLER) might have got away with murder lots of times (SERIAL KILLER),
18 A problem for those building snowmen (MELTING) at North Pole (compass POINT) (MELTING POINT) in a state where ice is dripping away (MELTING POINT),
21 Got the message (HEARD) from unfinished (t) hub (heart) (‘heart’ without ‘t’ = HEAR-) on delta (-D) (HEARD),
22 Anyone can (anyone can) go crazy (= anagram indicator) (anyone can = ANNOYANCE) with irritation (ANNOYANCE),
24 Puts on an act (PRETENDS) with unpredictable (= anagram indicator) serpent (serpent = PRETEN-S) around Dublin (-D-) (PRETENDS),
25 Starts a class action (starts ‘A Class Action’ = ACA-) with support (aid) coming back (= reversal indicator) (aid = -DIA) (ACADIA) from old French colony (ACADIA),
26 Sowing the seeds of (STARTING) agony (sting = ST-ING) over a (-A-) retweet (-RT-) (STARTING),
27 Small (S-) story (-TA-LE) about power (-P-) (STAPLE) that binds things together (STAPLE).
Down:
1 Cassette (cassette) produced (= anagram indicator) (cassette = TEST CASE) for the judge to hear setting a potential precedent (TEST CASE),
2 Some teasers with the primary actors (TRAILERS) from criminal (= anagram indicator) retrials (retrials = TRAILERS),
3 Over and above (EXTRA) former (EX-) beach in Ireland (Irish for ‘beach’ = trá = -TRA) (EXTRA),
5 Giving someone a rocket (DISCIPLINING) in a field of study (discipline) briefly (e) (‘discipline’ without ‘e’ = DISCIPLIN-) popular (-IN-) with Heisenberg’s Foundation (foundation/end of ‘heisenberG’ = -G) (DISCIPLINING),
6 Out at night, more so than usual (OVERSLEEP) – it’s what she might do awaiting the handsome prince (Sleeping Beauty OVERSLEEP),
7 In Paris where (French ‘where’ = OU-) time (-T-) and place (-PUT) (OUTPUT) is a measurement of one’s economic value (OUTPUT),
8 In Switzerland, calls (YODELS) to finish contemporary (finish ‘contemporarY’ = Y-) toys (models) starting off (m) (‘models’ without ‘m’ = -ODELS) (YODELS),
11 Advertise (market) the virtues of The Eden Project (MARKET GARDEN) for The Greens (MARKET GARDEN),
15 Qualification (AMENDMENT) for American (A-) repair (-MEND-) workers (-MEN-) at the end of employment (at the end of ‘employmenT’ = -T) (AMENDMENT),
16 Joined (SIGNED UP) Mark (SIGN-) getting in touch with English (-E-) party (Democratic Unionist Party = DUP = -D UP) (SIGNED UP),
17 It’s always poetic (e’er = -EER-) to be found in the play area (stage = ST-AGE) (STEERAGE) that’s not first class from a crafty perspective (STEERAGE),
19 Figures (SHAPES) in mist coming off steamships (‘mist’ coming off ‘steamships’ = seahps = SHAPES),
20 For the pictures (CAMERA) of a cream (a cream) pie (= anagram indicator) (a cream = CAMERA),
23 Cynthia drops in (‘Cynthia’ drops ‘in’ = cytha = YACHT) from the marina (YACHT).