Across:
1 Lose the head (b) in traffic (barter) (‘barter’ without ‘b’ = ARTER-) close to highway (close/end to ‘highwaY’ = -Y) (ARTERY) – an important major road (ARTERY),
4 Doesn’t show (OBSCURES) up (= reverse indicator) the stink created by individual (Body Odour = BO = OB-) getting top-secret (top ‘Secret’ = -S-) treatments (-CURES) (OBSCURES),
9 Outcome (RESULT) of Ulster (Ulster) Question? (= anagram indicator) (Ulster = RESULT),
10 Publius Vergilius Maro, for instance (aka Virgil = OLD LATIN), hasn’t been heard in Rome for a long time (OLD LATIN),
12 Step in (INTERVENE) for referee (INTERVENE),
13 Theatrical device (ASIDE is a theatrical device used by actors in a play) and switch (= reverse indicator) found in fire disaster (found in ‘firE DISAster’ = edisa = ASIDE),
14 Manager’s ribs (manager’s rib) damaged (= anagram indicator) (manager’s ribs = EMBARRASSING) and going red (EMBARRASSING),
18 Where one answers the call (TELEPHONE BOX) in ring (TELEPHONE) to fight (BOX) (TELEPHONE BOX),
21 Representative (AGENT) of a (A-) lady’s man (-GENT) (AGENT),
22 Hits (= anagram indicator) goalpost (goalpost = APOLOG-ST) bending around one (-I-) (APOLOGIST) making excuses for The Defence (APOLOGIST),
24 They hide what’s really happening (COVER-UPS) with mugs (C-UPS) boxing – it’s no longer on (-OVER-) (COVER-UPS),
25 Gore Vidal led away (‘Gore Vidal’ ‘led’ away/without ‘led’ = gorvia = VIRAGO) by bad-tempered woman (VIRAGO),
26 The dregs (RESIDUES) of bottle (= anagram indicator) is reused (is reused = RESIDUES),
27 It’s what many people get up to (breakfast CEREAL) in Clare? (CE-) That’s genuine! (-REAL) (CEREAL).
Down:
1 Broadcast (AIR-) from bar (-LINE-) with raw beginner (‘Raw’ beginner = -R) (AIRLINER) is bound to take off (AIRLINER),
2 Audition (TEST) leading thespians (leading ‘Thespians’ = T-) ahead of unit (ahead of ‘Unit’ = -U-) going to Belgium (-BE) (TEST TUBE) – and in that you will find your solution perhaps? (TEST TUBE),
3 A good measure (RULER) employed in The Palace (RULER),
5 Swan lake (Tchaikovsky’s Swan Lake = BALLET) with lots of carp (SCHOOL of fish) (BALLET SCHOOL) where one learns the intricacies of the fish dive (ballet dance move) presumably (BALLET SCHOOL),
6 Dishy type (COLCANNON) of officer (COL-) gets fired from headquarters perhaps (-CANNON) (COLCANNON),
7 In private, dismisses VIP? (‘in private’ dismisses ‘VIP’ = inrate = RETAIN) Keep that to yourself! (RETAIN),
8 One doing the numbers (SINGER) for OAP from Singapore (‘OAP’ from ‘ Singapore’ = singre = SINGER),
11 What a role model could do (SET AN EXAMPLE) for Irishman (Sean = SE- AN) over time (-T), when divorcee (EX-) has more than enough (-AMPLE) (SET AN EXAMPLE),
15 It’s about (RE-) direction to actor (-ENTER-) from writer (-ED) (RE-ENTERED) typed in on computer again (RE-ENTERED),
16 Turn your back (ABDICATE) on sailor (Able-Bodied seaman = AB-) taking lady friend (-D ATE-) around island (-I-) on top of craft (top of ‘Craft’ = -C-) (ABDICATE),
17 Those involved in psephology see this (EXIT POLL) as a way out (EXIT) for Count (POLL) (EXIT POLL),
19 Learn (learn = LAN-ER) exercise (= anagram indicator) around club (-C-) (LANCER) from one of those old fighters (LANCER),
20 In anyone’s book (LEAVES), the forecasters will read something into these (the forecasters/fortune-tellers will read something into these = tea LEAVES),
23 Duck (O-) liver (liver) is not finished (r) (‘liver’ without ‘r’ = -LIVE) (OLIVE) by one of The Greens (OLIVE green).