Across:
1 Tailor (MODIFY) and detective (-DI-) with leading fisherman (leading ‘Fisherman’ = -F-) in Mayo river (River Moy = MO-Y) (MODIFY),
4 Motivated (INSPIRED) insider (insider = INS-IRED) running (= anagram indicator) around park (-P-) (INSPIRED),
9 Spring back (RECOIL) for record (REC-) on Greece (‘Greece’ = ‘grease’ = -OIL) State (= homophone indicator) (RECOIL),
10 Enthusiastic applause (OVATIONS) as zero (O-) tax (-VAT-) is charged (-ION) for self-starter (‘Self’ starter = -S) (OVATIONS),
12 It’s beyond the bounds of possibilities (ILLOGICAL) unit (I-) lost (-L-) sound (-LOGICAL) (ILLOGICAL),
13 Characters in Odessa edited (characters in ‘OdesSA EDIted’ = saedi) Review (= reversal indicator) (saedi = IDEAS) of Theories (IDEAS),
14 Wasn’t lying (TOLD THE TRUTH) with this policy, didn’t activate any alarms in 18 down (TOLD THE TRUTH and didn’t activate ‘lie detectors’),
18 The make-up artists set them off presumably (LIE DETECTORS), as they recognise a good yarn when they hear it (LIE DETECTORS),
21 Part of the family from (UNCLE) a foreign (a = UN-) line (-L-) in Clare (-C-E) (UNCLE),
22 One (I-) tenor (-T-) in Belgian (Belgian = -GNI-ABLE) adaptation (= anagram indicator) (IGNITABLE) that’s likely to catch fire (IGNITABLE),
24 Page (HOME page) on flipping (= reversal indicator) Web (web = B-EW) includes writing (from the 3Rs = -R-) (HOME BREW) that’s heady and produced for personal consumption (HOME BREW),
25 Who in France (‘who’ in France = QUI-) joins party (Fianna Fáil = -FF-) at school (= -S) (QUIFFS)? Those getting pushed back by the Teddy Boys! (QUIFFS),
26 Pressure (P-) to find horse (horse = -GG-) in Irish (Irish = -RI-ISH) Free (= anagram indicator) (PRIGGISH) State that’s self-righteously important (PRIGGISH),
27 Women (W-) from hotel (-H-) drink (-ALE-) at the end of the pier (at end of the ‘pieR’ = -R) (WHALER) with Captain Ahab (Captain Ahab WHALER in Moby Dick).
Down:
1 Read aloud (= homophone indicator) grades (‘Marks’ = ‘Marx’ = MARX-) awarded by university (firsts = 1STS = -ISTS) (MARXISTS) to those studying Das Kapital (MARXISTS),
2 In a timid way (DOCILELY), medic (DOC-) takes ill (ill) briefly (l) (‘ill’ without ‘l’ = -IL-) near a place in Dublin (-ELY Place) (DOCILELY),
3 Cast (FLING) could be the inspiration for Love Story (FLING),
5 Working on the imaginative volume (NOVEL WRITING) with unorthodox (NOVEL) new (= anagram indicator) wiring (wiring = WRI-ING) over time (-T-) (NOVEL WRITING),
6 It (it = -TI-) is served up (= reversal indicator) in Capri to (Capri to = PATRIO-C) cast (= anagram indicator) (PATRIOTIC), produced with love for the country (PATRIOTIC),
7 Upset (= reversal indicator) some characters show ingratitude to Ireland (some characters show ‘ingratituDE TO IReland’ = detoir = RIOTED) and ran amok (RIOTED),
8 Stop (DESIST) taking trees out of side streets (taking ‘trees’ out of ‘side streets’ = sidest = DESIST),
11 Sounds like (= homophone indicator) Philip’s (‘Philips’ = ‘Phillips’ SCREWDRIVERS) orange juice and vodka drinks (SCREWDRIVERS),
15 Gent’s (gents = TOILET) satchel (BAG) (TOILET BAG) left in the cloakroom (TOILET BAG in cloakroom/toilet/bathroom),
16 Hard to believe (DOUBTFUL) suspect (DOUBT-) is loaded (full) for the most part (l) (‘full’ without ‘l’ = -FUL) (DOUBTFUL),
17 Fool (ASS-) showing off (= anagram indicator) roses (roses = -ESSOR) (ASSESSOR) in The Examiner (ASSESSOR),
19 Keep that under your hat (HUSH UP) or veil? (veil/conceal = HUSH UP),
20 Local rascal (SCAMP-) from institute (-I) (SCAMPI) produced something fishy (SCAMPI),
23 It’s therapeutic releasing a piece (‘therapeutic’ releasing ‘a piece’ = thrut = TRUTH) of honesty (TRUTH).