Across:
1 Piece (PISTOL) of plot is (plot is = PISTOL) outrageous (= anagram indicator),
4 Shafts (OBELISKS) boss-like (boss like = OBELISKS) criminal (= anagram indicator),
9 Take offence at (BRIDLE) Arabian headgear (BRIDLE Arabian horse headgear),
10 Cleaned up (CENSORED) dodgy (= anagram indicator) corn seed (corn seed = CENSORED),
12 The meaty type (RUMP STEAK) behind (RUMP) vocal (= homophone indicator) prop (prop/pole = ‘stake’ = ‘STEAK’) (RUMP STEAK’),
13 Those driven types (MINIS) immersed in feminism (immersed in ‘feminism’ = MINIS),
14 Most of those in 21 across (most of ‘wines’ = WINE) produced (= anagram indicator) anthem (anthem = ME-HANT) about religion (Roman Catholic = -RC-) (WINE MERCHANT) for one of The Libation Bearers (WINE MERCHANT),
18 Most of The Wire (most of the ‘tap’ = TA-) is a rip off (-STING) from student’s jottings (NOTES) (TASTING NOTES) – the types one associates with Port Authority? (TASTING NOTES),
21 They’re drunk (WINES) in all directions (west, north, east, south = W-NES) around the institute (-I-) (WINES),
22 What the police are likely to get up to (DAWN RAIDS) provides wake-up calls for the retired criminals (DAWN RAIDS),
24 It was taken from the first chap (first chap/Adam gave SPARE RIB to Eve) with extra (SPARE) small, open boat (RIB) (SPARE RIB),
25 Cannot leave non-addictive (‘cannot’ leave/leaving ‘non-addictive’ = ddiive = DIVIDE) type of order (DIVIDE),
26 Similar (PARALLEL) to a (-A-) couple of lines (-LL-) in pearl (pearl = PAR-EL) dress (= anagram indicator) (PARALLEL),
27 Board member (chess board KNIGHT) to consider (consider = think = KNI-HT) retiring (= reversal indicator) around end of spring (end of ‘spring’ = -G-) (KNIGHT).
Down:
1 Creep (CRAWL) follows (= positional indicator) a stout dealer (PUB) (PUB CRAWL) on local tour (PUB CRAWL),
2 Carol (S-ING) entertains women’s organisation (Women’s Institute = -WI-) and Frenchmen (Messieurs = -MM-) (SWIMMING) going overseas (SWIMMING),
3 Crudely checks out (OGLES) the lanes coming out of Los Angeles (‘lanes’ coming out of ‘Los Angeles’ = osgle = OGLES),
5 Expose story (BREAK THE NEWS) of what one could do with scoop (BREAK THE NEWS),
6 Traditionally, the first one out (LAST MAN IN is the first out) with head tracker (head ‘tracker’ = -T-) consumed by wild (= anagram indicator) animals (animals = LAS- MAN I-) at end of autumn (end of ‘autumn’ = -N) (LAST MAN IN),
7 Short (g) season (‘spring’ without ‘g’ = SPRIN-) for first team (first ‘team’ = -T) (SPRINT) in Rush (rush = SPRINT),
8 Samuel (SA-M) conceals Diana’s (Di’s = -DIS-) (SADISM) humiliating cruelty (SADISM),
11 Get a lesson on how to handle vehicle (LEARN TO DRIVE) for Shakespearean character (LEAR-) not (not = -N TO) out (= anagram indicator) to do what’s expected of swinger (swinger/golfer / DRIVE) (LEARN TO DRIVE),
15 The average (average/middle course = MEAN-) Dandy in America (dandy/swell = -S WELL) (MEANS WELL) has good intentions (MEANS WELL),
16 Prominent type (STRIKING type) giving up on Labour, as it’s not working (STRIKING),
17 In my opinion (AS I SEE IT), other spies can’t get their heads around my view (AS I SEE IT),
19 Admits (OWNS UP) Eoin is awake (“Eoin’s up” = “OWNS UP”) for the audience (= homophone indicator),
20 Not just (UNFAIR) for fun (fun = UNF-) run (= anagram indicator) – it’s for broadcast (-AIR) (UNFAIR),
23 Rule (REIGN) from base off Bering Sea (‘base’ off ‘Bering Sea’ = REIGN).