Across:
1 Issues (COPIES) with what’s at the end of 14 across (‘master copies’ = COPIES),
4 Take a draw (SMOKE) when not at home (OUT) (SMOKE OUT) – with this approach there’s no hiding place (SMOKE OUT),
9 Opens 14 across (‘master copies’ = MASTER) in Liège? (liege lord = MASTER),
10 One way to watch television (ON DEMAND) play (= anagram indicator) – and men do (and men do = ON DEMAND),
12 Handyman primarily (‘handyman’ primarily = H-) tunes (-AIRS-) piano (-P-) in school (-RAY) (HAIRSPRAY) with aerosol (aerosol HAIRSPRAY),
13 It’s not right (FALSE) to chop up (= anagram indicator) fleas (fleas = FALSE),
14 Original recordings (MASTER COPIES) by expert (MASTER) on apes (COPIES) (MASTER COPIES),
18 Sounds like residencies for The Three Sisters (nursing sisters in NURSING HOMES) and those looking after the welfare of Old Vic, among others (NURSING HOMES),
21 Must get out of Mousetrap (take ‘must’ out of ‘Mousetrap’ = oerap = OPERA) and Madame Butterfly (Giacomo Puccini’s Madame Butterfly = OPERA),
22 What’s trending (what’s IN) is intrinsic (ESSENCE) (IN ESSENCE) when all is said and done (IN ESSENCE),
24 Large numbers (MILLIONS) to exploit (milk) for the most part (k) (‘milk’ without ‘k’ = MIL-) for those with pride (-LIONS) (MILLIONS),
25 Reds removed from barricades, (‘reds’ removed from ‘barricades’ = barica = ARABIC) in a manner of speaking (ARABIC),
26 Sporting lady paid out (“sporting lady” “paid” out = sortngly = STRONGLY) solidly (STRONGLY),
27 In part, Christian Gershwin (in part ‘Christian Gershwin’ = ANGERS) rubs people up the wrong way (ANGERS).
Down:
1 What the Prodigal Son could do (COME HOME) to show up (COME) The House (HOME) (COME HOME),
2 The most assertive (PUSHIEST) nuisance (P-EST) admits my group (-US-) is mostly (p) cool (‘hip’ without ‘p’ = -HI-) (PUSHIEST),
3 Remove snip from winepress (remove ‘snip’ from ‘winepress’ = weres = EWERS) and jugs (EWERS),
5 Lucrative enterprise (MONEY-SPINNER) in capital (MONEY) for evil-doer (S-INNER) handling pressure (-P-) (MONEY-SPINNER),
6 Chill (KEEP FRESH) in brand new (FRESH) castle (KEEP) from the start (= positional indicator) (KEEP FRESH),
7 Prophet (ORACLE) or a cleric concealed in part (‘or a cleric’ concealed in part = ORACLE),
8 Picked up (TIDED) ahead of traffic (ahead of ‘traffic’ = T-) island (-I-) and then (= positional indicator) conked out (-DIED) (TIDIED),
11 Hymn (PROCESSIONAL) with a (-A-) line (-L) that comes after (= position indicator) parade (PROCESSION-) (PROCESSIONAL),
15 Cautioned (cautioned = EDUCATION) playing (= anagram indicator) in the classy practice for those in the academy (EDUCATION),
16 Cooperative (AMENABLE) is prepared to (A-BLE) cover workers (-MEN-) from association (-A-) (AMENABLE),
17 Extracts (ESSENCES) from the end of 22 across (‘in essence’ = ESSENCE-) and the end of The Troubles (and the end of ‘The Troubles’ = -S) (ESSENCES),
19 Take a couple of breaths in the passage (punctuation marks in passage/book extract = COMMAS) – it could be the butterflies? (butterflies = COMMAS),
20 Is getting out of Carlisle (‘is’ getting out of ‘Carlisle’ = carlle = CELLAR) for a basement in Bordeaux (CELLAR),
23 Father (SIRE-) last seen (last ‘seen’ = -N) (SIREN) on top of the Garda car (SIREN).