Across:
1 Is responsible for the number on the street (BUSKER) and for publicly airing what’s at end of 14 across (publicly airing what’s at end of ‘face the music’ = BUSKER),
4 Grim (DREADFUL) study (-READ-) opens Family Unit (opens ‘Family Unit’ = -FU-) set in Donegal (D-L) (DREADFUL),
9 Paul (Paul = UPL-A-) Rock (= anagram indicator) welcomes order (-O-) from director (-D) (UPLOAD) to release it on the Internet (UPLOAD),
10 Application (APP-) draws attention (Oi! = -OI-) to good books (New Testament = -NT-) with small (-S) (APPOINTS) names (APPOINTS),
12 Stolen (HOT) drugs (POT-) from a (-A-) fair amount of (half of) the town (half of ‘town’ = -TO) (HOT POTATO) leads to a locally controversial issue (HOT POTATO),
13 Canoe (canoe = OCEAN) out of place (= anagram indicator) in large body of water (OCEAN),
14 Side (facet = FACE T-) with that man (-HE) taking rap (rap MUSIC) (FACE THE MUSIC) and accept responsibility (FACE THE MUSIC),
18 What man upstairs will do on the final day (RAISE THE DEAD) to bring up (RAISE) Joyce’s book (James Joyce’s The Dead = THE DEAD) (RAISE THE DEAD),
21 Cicero is taken from police court (‘Cicero’ is taken from ‘police court’ = polut = PLUTO) by mythical figure from the underworld (god of underworld = PLUTO),
22 Exhibition (SHOW) by 23 down (“house’ = HOUSE) (SHOW HOUSE) gives one the impression of where we might be living in the future (SHOW HOUSE),
24 It’s an utter failure (DISASTER) to set-up (= reversal indicator) Sidney (Sid = DIS-) with Daisy’s relative (-ASTER) (DISASTER),
25 Scrum (TUSSLE) in Donnybrook (scene of donnybrook/disorder = TUSSLE),
26 Consider in a different light (REASSESS) most of the (l) actual (“real” without “l” = REA-) engineering (-E-) found in two ships (SS-SS) (REASSESS),
27 Crazy (= anagram indicator) estate (estate = TEA SET) for the Mad Hatters (TEA SET).
Down:
1 Rejection of someone (BRUSH-OFF) born (B-) near Dublin suburb (-RUSH) is bad (-OFF) (BRUSH-OFF),
2 Breaking up (=anagram indicator) soils, etc., (soils etc = SOLSTICE) comes at a turning point in the summer (SOLSTICE),
3 Some deliver a token (some “deliver a token” = ERATO) source of inspiration (Muse of lyrical poetry / source of inspiration = ERATO),
5 Director (-D-) in Puerto Rico (Puerto Rico = REPRO-UCTIO-) adapting (= anagram indicator) first novel (first ‘novel’ = -N) (REPRODUCTION) – the one that’s a fake (REPRODUCTION),
6 Sorry about this (APOLOGISE), as it’s a (A-) bit of horseplay (-POLO-) for soldiers (GIs = -GIS-) from Spain (-E) (APOLOGISE),
7 First opening (‘first’ opening = F-) scene (scene = -ENCES) mixed-up (= anagram indicator) (FENCES) by those defining the parameters around The Gate (FENCES),
8 Take cab from log cabins (take ‘cab’ from ‘log cabins’ = logins = LOSING) giving someone the slip (LOSING),
11 Found in 13 across (found in ‘ocean” = WATER) and computer networks (SYSTEMS) (WATER SYSTEMS) by those working on their drinking problems perhaps (WATER SYSTEMS),
15 Opens 27 across (opens ‘tea set’ = TEA-) and more than one of those from 23 down (more than one ‘house’ = HOUSES) (TEAHOUSES) in Oriental cafés (TEAHOUSES),
16 Demands (REQUESTS) what 1 across might be asked to perform (REQUESTS is what ‘busker’ might be asked to perform),
17 He daren’t (he daren’t = ADHERENT) cross (= anagram indicator) supporter (ADHERENT),
19 Trim (y) agent (‘spy’ without ‘y’ = SP-) is from institute (-I-) with the German (the = -DER) (SPIDER) web designer (SPIDER),
20 Old European kingdom (Prussia) loses head (p) (‘Prussia’ without ‘p’ = RUSSIA) with Georgian neighbour (RUSSIA),
23 Share out missing art (‘share out’ missing ‘art’ = sheou = HOUSE) and put up (HOUSE).