The ten unclued lights consist of a theme word and three groups of three answers of a kind, each group relating differently to the theme word. Unchecked and cross-checking letters in these answers could make TAX AUDITOR APPROVE.
 

Across

 
1    Cuttingly, John dissects fancy style (8)
10    Escape with loot is dicey in Catholic’s area (12, two words)
13    Two pianos are for old man (7)
17    One eats a bit with a king and queen (8)
21    Chemist’s glum with rain streaming (8)
23    Little 4 blocks hearing (7)
25    Where to learn one plus one (3)
29    Excitable, touring Crete and French island (8)
34    Rotating arms and head gives comfort (8)
35    Bum steer, regularly? That’s right (4)
36    Sailor wasted cash for ammoniac plants (6)
39    Traitor cheers about finding oil (5)
40    Journo goes over case with title (12)
41    Choreographer has reinvented fashion (6)
42    Climbers’ entries in opera house parties (8)
 

Down

 
1    Mariner with reportedly safe compound (9)
2    Great English artwork (4)
3    Like headless god originating in itself (6)
5    Having left road, poor reversing in Welsh town (8)
6    Leaders in science scoff about tests (7)
7    American leaves people in household to mix (5)
8    Rejects regressive idiot, one cutting tax (10)
9    Bite ends of garden remains (5)
11    Run-down Balls bound to defend Labour, ultimately (9)
14    Runner enters hall with salad ingredient (7)
18    Improves image of Serbia, nimbly protecting race (10)
19    Musical groups from Norway visiting fairly dry island (9)
20    Resisting force without resistance — it can’t be true (7)
22    Calms down extremely rare equid and old oxen (9)
24    Wearing coat, current Hamlet rises up like a fury (8)
27    Division of racing boat no-one backed (7)
31    Orange eaten by man at table (6)
32    Have meal with divine sun above (5)
33    Engineers stopping to obtain address (5)
 
A first prize of £30 for the first correct solution opened on 24 November. There are two runners-up prizes of £20. (UK solvers can choose to receive the latest edition of the Chambers Dictionary instead of cash — circle the word ‘Dictionary’.) Entries to: Crossword 2187, The Spectator, 22 Old Queen Street, London SW1H 9HP. Please allow six weeks for prize delivery.