Across:
1 Lost (-L-) in class (caste = CAST-E) (CASTLE) in the big house perhaps (CASTLE),
4 Picked up (OBTAINED) first of the onions (first of the ‘Onions’ = O-) that ain’t (aint = -TAIN-) fresh (= anagram indicator) coming out of plot (-B-ED) (OBTAINED),
9 Loses rag in Argentina (loses ‘rag’ in ‘Argentina’ = entina = INNATE) – it’s something one does without thinking (it’s INNATE),
10 Rewrite (= anagram indicator) grey tome (grey tome = GEOMETRY) for maths class (GEOMETRY),
12 Type of builder (COWBOY) on the board of monopoly (HAT token in monopoly board game) (COWBOY HAT) keeps a cool head out west (COWBOY HAT),
13 Reynolds dismisses sly (‘Reynolds’ dismisses ‘sly’ = renod = DRONE) type with no sting in tail (DRONE),
14 One will never get over (INCONSOLABLE) how that popular (IN-) backward (= reversal indicator) graduate (BA = -AB-) is left (-L-) in control of the game (console = -CONSOL-E) (INCONSOLABLE),
18 Has a job examining relative’s (FAMILY DOCTOR) bloodline (FAMILY) for Spike (spike/tamper = DOCTOR) (FAMILY DOCTOR),
21 Grant (AWARD) for area (A-) in the hospital (-WARD) (AWARD),
22 The exceptions to the rules (GREY AREAS) of break-up (= anagram indicator) – Ray agrees (Ray agrees = GREY AREAS),
24 Cynthia (Cynthia = HYACINT-) arranged (= anagram indicator) to visit hospital (-H) (HYACINTH) with plant from Lily (HYACINTH),
25 Raise a stink dismissing saint (‘raise a stink’ dismissing ‘saint’ = raisek = KAISER) – a holy roman emperor (KAISER),
26 They rack their brains (THINKERS) for the names of philosophers (THINKERS),
27 Ran away from guardsmen (‘ran’ away from ‘guardsmen’ = gudsme = SMUDGE) with Mark (mark = SMUDGE).
Down:
1 Greek letter (CHI-) is not the first (‘Not’ the first = -N-) Greek letter (CHI-) to new (-N) (CHIN-CHIN) and to absent friends (to absent friends = a toast = CHIN-CHIN),
2 Makes a meal (SANDWICH) of gritty stuff (SAND-) coming from women’s organisation (Women’s Institute = -WI-) connected to church (-CH) (SANDWICH),
3 Beverage from root vegetable? (‘beverage’ from ‘root vegetable’ = oottl = LOTTO) Bingo! (LOTTO),
5 The police use this to look for the blow (BREATHALYSER) by detecting what’s in 15 down (detecting what’s in ‘neat drink’ = BREATHALYER),
6 Beastly type (ARMADILLO) of new (= anagram indicator) drama (drama = ARMAD-) is not up to par (-ILL-) – nothing is? (nothing is ‘zero’ = -O) (ARMADILLO),
7 It’s not (NOT-) on (-ON) after (= position indicator) institute (-I-) (NOTION) gets wrong impression perhaps (NOTION),
8 Key (music key D-) to playing (= anagram indicator) nerdy (nerdy = -RYDEN) (DRYDEN) old poet (DRYDEN),
11 Is this what the director is expecting to do (SHOOTING STAR) travelling light? (SHOOTING STAR),
15 Shipshape (NEAT) at the top of the dock (at the top of the ‘Dock’ = D-) where there’s ice (-RINK) (NEAT DRINK) in port with no water (NEAT DRINK),
16 Under pressure (STRESSED) to reorder (= anagram indicator) dresses (dresses = S-RESSED) over time (-T-) (STRESSED),
17 Keep (PRESERVE) page (P-) from book (-RESERVE) (PRESERVE),
19 Status (CACHET) of a (-A-) revolutionary (-CHE-) in court (C-T) (CACHET),
20 No permit in Maritime Alps (no ‘permit’ in ‘Maritime Alps’ = aimals = SALAMI) for cured sausage (SALAMI),
23 A wake-up call (ALARM) for team sacrificed by Alma Mater (‘team’ sacrificed by ‘Alma Mater’ = almar = ALARM).