Across:
1 A (A-) tax (-VAT- tax) on artist (RA) retiring (= reversal indicator) (RA = -AR) (AVATAR) as virtual icon (AVATAR),
4 Make rice (make rice) dish (= anagram indicator) (make rice = ICE MAKER) and keep it in the freezer (ICE MAKER),
9 Recognised there’s no need (‘recognised’ without ‘need’ = rcogis = CORGIS) for dogs (CORGIS),
10 Altogether sounded like one (IN UNISON) popular (IN), small place of learning (small university = UNI-) for one of those in Trinity (-SON is in The Holy Trinity) (IN UNISON),
12 The first one out of the blocks (PACEMAKER) is March (PACE-), the last in 4 across (last in ‘ice maker’ = -MAKER) (PACEMAKER),
13 Song and dance (SCENE) witnessed in the abbey (SCENE in The Abbey Theatre),
14 Sounds like the sound of Little Feat (sounds like the sound of ‘Little Feat’ = ‘little feet’ = PITTER-PATTER) drumming (PITTER-PATTER),
18 Unwell (-ILL-), in pain (ache = ACH-E-), savage head (‘Savage’ head = -S) and on foot (HEEL) (ACHILLES HEEL) – and this is supposed to be one’s main weakness? (ACHILLES HEEL),
21 Sweetheart (‘swEet’ heart = -E-) in family (CL-AN) (CLEAN) is off the drugs (CLEAN),
22 Local cop out (GET AROUND) of Dodge? (GET AROUND),
24 Line (COR-D-) about most of (p) the last letters (‘RIP’ without ‘p’= -RI-) from old (-O-) writing (from the 3Rs = -R) (CORRIDOR) passage (CORRIDOR),
25 Key (music key -G-) found in building (= anagram indicator) opens (opens = SPON-E) (SPONGE) one of those in the bakery (SPONGE),
26 Authorised (ENTITLED) wind-up (EN-D) over ownership (-TITLE-) (ENTITLED),
27 Relative of Daisy’s (ASTER-) not the first (‘Not’ the first = -N) (ASTERN) back from the navy? (ASTERN).
Down:
1 Gardaí (cops = -COP-S) incorporating minor operation (-OP-) following gangster (AL- Capone) (ALCOPOPS) offering drinks to locals (ALCOPOPS),
2 It’s an outrage (ATROCITY) starting off from (a) main artery (‘aorta’ without ‘a’ = orta) going up (= reversal indicator) (orta = ATRO-) to Dublin, for example (-CITY) (ATROCITY),
3 Heard (= homophone indicator) principal (‘principal’ = ‘principle’ = AXIOM) accepted truth (AXIOM),
5 Well-done (well done = CONGRATULATE) toast? (CONGRATULATE),
6 Miser isn’t (miser isn’t) recycling (= anagram indicator) (miser isn’t = MINISTERS) contents of cabinet (MINISTERS),
7 Barely touched (barely touched/brushed off = KISSED) ale from lakesides (‘ale’ from ‘lakesides’ = ksides = KISSED),
8 Play (RENDER) cover of The Stones (RENDER),
11 One of those in the gym (SKIPPING ROPE) is missing (SKIPPING) most of those in 23 down (most of ‘ropes’ = ROPE) (SKIPPING ROPE),
15 Put away (-CONVICT) after (= position indicator) old partner (EX -) (EX-CONVICT) is no longer confined (EX-CONVICT),
16 Clip (SEQUENCE) of Hyde, O’Kelly and de Valera, for example (SEQUENCE of Irish Presidents),
17 Slightly give in (budge = B-UDGE-) over fillets, heart (‘filLets’ heart = -L-) and first two onions (first two ‘ONions’ = -ON) (BLUDGEON) in batter (batter/hit = BLUDGEON),
19 DNA removed from Icelandic (‘DNA’ removed from ‘Icelandic’ = icelic = ICICLE) spike that’s frozen (ICICLE),
20 No pubs in Petersburg (no ‘pubs’ in ‘Petersburg’ = eterrg = REGRET) – I don’t like the sound of that? (REGRET),
23 Prose (prose) novel (= anagram indicator) (prose = ROPES) with ties to Ring (ties to boxing ring = ROPES).