Across:
1 Annoying type (GADFLY) of grotesque, extreme (‘grotesque’ extreme = G-) advertisement (-AD-) on Dart (dart/dash = -FLY) (GADFLY),
4 Independent (I-) state (= homophone indicator) figure from Finance (“sum” = “some” = -SOME-) to test (-TRY) (ISOMETRY) similar measures (ISOMETRY),
9 Danish (Danish PASTRY) model (= anagram indicator) parts (parts = PASTR-) with Yankee (-Y) (PASTRY),
10 Senses (MEANINGS) popular (-IN-) legend (“leg” end = -G-) consumed by wealth (MEAN- S) (MEANINGS),
12 Award from university (first = 1st = -IST) after (= positional indicator) life’s study (biology) cut short (y) (‘biology’ without ‘y’ = BIOLOG-) (BIOLOGIST) by one of those concerned with evolution (BIOLOGIST),
13 Wildlife park (zoo = -OOZ-) set up (= reversal indicator) in Belgium (B-E) (BOOZE) by those in good spirits presumably (BOOZE),
14 A chap that’s never in the public eye (INVISIBLE MAN) won’t leave a trace of his movements (INVISIBLE MAN),
18 Ignore (DISCOUNT) college (C-) in the forest (-ASH) opening (= positional indicator) (CASH DISCOUNT) for those interested in better terms (CASH DISCOUNT),
21 Nips away from Parisians (‘nips’ away from ‘Parisians’ = arias = ARIAS) coming out of Palais Garnier, for example (ARIAS),
22 Macho types (he-men = -HEMEN-) in Venice missing Northern Ireland (NI) (‘Venice’ missing ‘NI’ = VE-CE) (VEHEMENCE) force (VEHEMENCE),
24 Leaving (GOING-) one of those in Trinity (one in The Trinity: Father, Son and Holy Spirit = -S ON) (GOINGS-ON) synonymous with dodgy behaviour (GOINGS-ON),
25 Outstanding (UNPAID) organisation (UN-) put up the cash (-PAID) (UNPAID),
26 A Reuter’s (a Reuters = TREASURE) misprint (= anagram indicator) – I’d dig a hole to conceal that! (TREASURE)
27 Ain’t leaving great-niece (‘aint’ leaving ‘great-niece’ = greece = GREECE) in the Mediterranean (GREECE).
Down:
1 Strange (= anagram indicator) logic (logic = GO -LIC) obstructing bar (PUB-) (GO PUBLIC) for those who want to open up (GO PUBLIC),
2 Detectives (DIs = DIS-) work out (-SOLVE) (DISSOLVE) and wind down (DISSOLVE),
3 Slow movement (LARGO) of large (L-) mythical ship (-ARGO) (LARGO),
5 Realises the error of one’s way (SEES THE LIGHT) in rant (seethe = SEE- THE) about Old Bob (old bob = shilling = -S) – a traffic controller (traffic LIGHT) (SEES THE LIGHT),
6 Criminal (= anagram indicator) conman (conman = MON- -ANC) admits bacterial disease (-T B-) on top of lumbago (on top of ‘lumbago’ = -L-) (MONT BLANC) is a mountain to climb (MONT BLANC),
7 Drive crazy (-ANNOY) behind (= positional indicator) car (model T-) (TANNOY) with sound system (TANNOY),
8 Of course (YES -), that lot on stag party (-MEN) (YES- MEN) can never say no (YES-MEN),
11 Manufactures Irish shirts, tops (‘manufactures Irish shirts’ tops = MIS-) and habits (BEHAVIOUR) (MISBEHAVIOUR) for Bad Manners (MISBEHAVIOUR),
15 Leading actor (STAR) from The Omens (SIGNS) (STAR SIGNS), The Bull and The Water-Bearer (STAR SIGNS),
16 Switch (TURN) port (P-) for beer (-ALE) (TURN PALE) – it might be your response if you see one of the spirits perhaps (TURN PALE),
17 Last (= positional indicator) drugs (EEs = -EE) deal with (ATTEND- to) (ATTENDEE) partygoer (ATTENDEE),
19 Mark (mark = TARGET) immersed in Gibraltar getaway (immersed in’ Gibraltar getaway’ = TARGET),
20 It’s limited (FINITE) to one (-I-) time (-T-) in Dandy (Dandy! = FIN-E) (FINITE),
23 It’s dismissed by minister (‘its’ dismissed by minister’ = miner = MINER) as a job for one of those gold-diggers in Labour (gold-diggers in labour/work = MINER).