Across:
1 Nuts thrown by debutantes (‘nuts’ thrown by ‘debutantes’ = debate = DEBATE) gets people talking (DEBATE),
4 Lodges (CHAPTERS) with fellows (CHAP-S) over academic period (term) briefly (m) (‘term’ without ‘m’ = -TER-) (CHAPTERS),
9 A (A-) scene (-VENUE) (AVENUE) out of The Road (AVENUE),
10 Orchestral leader (‘Orchestral’ leader = O-) produces bass (-B-) violin (violin) movement (= anagram indicator) (violin = -LIVION) (OBLIVION) from forgotten state (OBLIVION),
12 Alpine (ROCK PLANT) type of music (ROCK) schedule (PLAN-) for opening of Tradfest (opening of ‘Tradfest’ = -T) (ROCK PLANT),
13 Dudley Moore releases medley (‘Dudley Moore’ releases ‘medley’ = udoor = ODOUR) with an unpleasant air (ODOUR),
14 Major development (BREAKTHROUGH) to fracture (BREAK-) state? (= homophone indicator) Correct! (‘true’ = ‘through’ = -THROUGH) (BREAKTHROUGH),
18 Broadcast picked up (TRANSMISSION), in part, in the car (car TRANSMISSION),
21 Man from Munster (man from Münster in Germany = Herr) loses the head (h) (‘herr’ without ‘h’ = -ERR-) in very important (key = KE-Y) (KERRY) county of Ireland (KERRY),
22 Tehran bus (Tehran bus) broken (= anagram indicator) (Tehran bus = SUNBATHER) down on the beach (SUNBATHER),
24 Artist (RA = R-A-) admits first victim (-ABEL- murdered by Cain in The Bible) is (-IS) (RABELAIS) an old comic French writer (RABELAIS),
25 Short (t) clue (‘hint’ without ‘t’= -HIN-) in garden plot (bed = BE-D) (BEHIND), of late (BEHIND),
26 Old toffee (NONSENSE) from Blarney (NONSENSE),
27 Get to grips with (MASTER) meandering (= anagram indicator) stream (stream = MASTER).
Down:
1 Stream of abuse? (DIATRIBE) Or rising (= reversal indicator) support (aid = DIA-) for one of those in Galway! (Galway Tribesmen = -TRIBE) (DIATRIBE),
2 Revolutionary (-CHE-) consumed by local money (BREA-D) (BREACHED) in Split (BREACHED),
3 Top (TRUMP) bone (T- bone) from piece of meat (-RUMP) (TRUMP),
5 Presumably this is what wardrobe mistress in The Abbey is doing (presumably this is what wardrobe mistress in the abbey is doing = HABIT-FORMING) and it’s addictive (HABIT-FORMING),
6 Clip (e) of Grace (poise) (‘poise’ without ‘e’ = POIS-) playing (= anagram indicator) a song (a song = -ON GAS) (POISON GAS) by one of The Killers on the airwaves (POISON GAS),
7 Runs daily (EDITOR) and rides out without us (‘rides out’ without ‘us’ = rideot = EDITOR),
8 Criminal (= anagram indicator) rents (rents = SENTR-) yard (-Y) (SENTRY) from guard (SENTRY),
11 Graduate (BA-) to object (object/item = -THING) to those in the pack (SUITS in pack of cards) (BATHING SUITS) or those appealing to 22 across (BATHING SUITS appealing to ‘sunbather’),
15 Terrier (KERRY BLUE terrier) from 21 across (‘kerry’ = KERRY) and Down (down/sad = BLUE) (KERRY BLUE),
16 Things you’d like to have (WISH LIST) whilst (whilst = WISH L-T) out (= anagram indicator) around island (-I-) going towards The Point (South = -S) (WISH LIST),
17 Trendy (IN-) town leader (‘Town’ leader = -T-) is cheeky (-RUDE-) writing (from the 3Rs = -R) (INTRUDER) to one of those breaking into the business (INTRUDER)
19 Ruskin (Ruskin) mixing (= anagram indicator) (Ruskin = SKI RUN) track on a slope (SKI RUN),
20 Take hold of (GRAB-) key (music key -E-) to accommodation on one side (‘accommodatioN’ on one side = -N) (GRABEN) block, that has its faults? (elongated block of the earth’s crust lying between two faults = GRABEN),
23 Ballerina ignores bill (‘ballerina’ ignores ‘bill’ = aerna = ARENA) from the sports hall (ARENA).