Across:
1 Teased (teased) model (= anagram indicator) (teased = SEDATE) with dope (SEDATE),
4 Armadillo, for instance (EDENTATE), from The Garden (Garden of EDEN-) State needs no introduction (s) (‘state’ without ‘s’ = -TATE) (EDENTATE),
9 At the end of Gladiator (end of ‘gladiatoR’ = R-), Ollie (Ollie) briefly (e) (‘Ollie’ without ‘e’ = -OLL I-) is the last person (last ‘persoN’ = -N) (ROLL IN) to show up as the fog descends (ROLL IN),
10 Set (set) play (= anagram indicator) (set = EST-) for one (-I-) pal (-MATE) (ESTIMATE) – a ballpark figure (ESTIMATE),
12 Samples (PORTFOLIO) drink (PORT-) with duck (-O-) in filo (filo) bake (= anagram indicator) (filo = F-LIO) (PORTFOLIO),
13 Pays attention to (HEEDS) rib leaving Hebrides (‘rib’ leaving ‘Hebrides’ = hedes = HEEDS),
14 Has a job examining relative’s (FAMILY DOCTOR) bloodline (FAMILY) for Spike (spike/tamper = DOCTOR) (FAMILY DOCTOR),
18 Those taken by Constable perhaps (taken by constable/police = FINGERPRINTS) in 27 across (‘finger’ = FINGER-) and 20 down (‘prints’ = -PRINTS) (FINGERPRINTS),
21 Loses the head (p) on drink (‘port’ without ‘p’ = -ORT-) and goes into Alcoholics Anonymous (A-A) (AORTA) – will the cardiologist be able to handle it? (AORTA),
22 Fine (fine) criminal (= anagram indicator) (fine = INEF-) for false statement? (-FABLE) (INEFFABLE) It’s beyond words! (INEFFABLE),
24 Colourful type (GUNMETAL) of piece (GUN-) on square (-T- square) meal (meal = -ME-AL) doing the rounds (GUNMETAL),
25 Auntie (auntie) broadcasted (= homophone indicator) (‘auntie’ = ‘anti’ = ANTI-) college (-C-) and school (-S) (ANTICS) pranks (ANTICS),
26 Final (LAST), final warning (final ‘warninG’ = G-) for snaky type (-ASP) (LAST GASP) sounds like a touch of desperation (LAST GASP),
27 One of those on hand (FINGER) to dig it? (‘dig it’ = ‘digit’ = FINGER).
Down:
1 Remove the gear (STRIP OFF) from small (S-) dandy (toff = -T- OFF) from Split (-RIP) (STRIP OFF),
2 The Party (DO-) line (-L-) – they can be beat (-DRUMS) (DOLDRUMS) – out of despondency (DOLDRUMS),
3 Criminal (THIEF) institute (-I-) mentioned in article (TH-E-) on French capital (‘French’ capital = -F) (THIEF),
5 Taken by surprise (DISCONCERTED) by theologian (DD = D-D) welcoming one (-I-) small (-S-) musical performance (-CONCERT-) by One Direction (East = -E-) (DISCONCERTED),
6 No sodas in boarding houses (no ‘sodas’ in ‘boarding houses’ = boringhue = NEIGHBOUR) for one of those next door (NEIGHBOUR),
7 Cools off (ABATES) most getting off steamboats (‘most’ getting off ‘steamboats’ = steaba = ABATES),
8 In spite of that (EVEN SO), run (r) out of courage (nerve) (‘r’ out of ‘nerve’ = neve), flip (= reverse indicator) (neve = EVEN) and cry (sob) briefly (b) (‘sob’ without ‘s’ = SO) (EVEN SO)
11 Shown on a projector (SLIDE) to swingers (Golf Union of Ireland = GUI-), sailors (-TARS) (SLIDE GUITARS) and those plucky types who are capable of pulling strings (SLIDE GUITARS),
15 Created an issue (offspring) by using white silkies (white silkies = chickens) (issue/offspring from chicken / LAID AN EGG) – could Humpty Dumpty have done this for someone’s breakfast? (LAID AN EGG),
16 Rudely ignoring someone (SNUBBING) serving up (= reverse indicator) small cakes (buns = SNUB-) with a type of cherry (-BING cherry) (SNUBBING),
17 Judge (ASSESSOR) from Rosses (Rosses = -SESSOR) Point (South = -S-) area (A-) going all the way back (= reverse all indicator) (ASSESSOR),
19 Sounds like (= homophone indicator) a type of beat (‘beat’ = ‘beet’ = MANGEL) – a staple of The Animals (stock feed = MANGEL),
20 Pictures (PRINTS) of sprint (sprint) runner (= anagram indicator) (sprint = PRINTS),
23 Clip (‘e’) of missing dolphin (‘Fungie’ without ‘e’ = FUNGI) from poison fire coral, for instance? (type of deadly FUNGI).