Across:
1 Crime overseas (PIRACY) in Capri (Capri) damaging (= anagram indicator) (Capri = PIRAC-) contemporary foundation (‘contemporarY’ foundation = -Y) (PIRACY),
4 Make up (make-up = LIPSTICK) with mouthy type (LIP-) getting grief (-STICK) (LIPSTICK),
9 Taunt (taunt) criminal (= anagram indicator) (taunt = ATTUN-) to start embezzling (start ‘Embezzling’ = -E) (ATTUNE) from tailor (tailor/adjust = ATTUNE),
10 Passage (CORRIDOR) in tape (tape/cord = COR-D-) covering border (rim) is cut (m) (‘rim’ without ‘m’ = -RI-) along with old (-O-) writing (from the 3Rs = -R) (CORRIDOR),
12 Discharge (SACK-) from dust collector (-CLOTH) (SACKCLOTH) produced by Ashe’s partner (‘SACKCLOTH and ashes’),
13 Prince (NOBLE) and One Direction (North = N-) on short (w) Elbow (‘Elbow’ without ‘w’ = elbo) backtrack (= reverse indicator) (elbo = -OBEL) (NOBEL),
14 Introduction to 18 across (introduction to ‘bank holidays’ = BANK) linked to books (RESERVES) (BANK RESERVES) kept back in safe places in case of financial crisis (BANK RESERVES),
18 Work breaks (HOLIDAY-) in places of interest (banks = BANK -S) (BANK HOLIDAYS) after Christmas and after Easter (St. Stephen’s Day and Easter Monday = BANK HOLIDAYS),
21 What is ahead of many a team facing The Hill (CLIMB) in cold (C-) with life partner (life partner = ‘life and limb’ = -LIMB) (CLIMB)
22 Try hard (ENDEAVOUR) flying (= anagram indicator) over a dune (over a dune = ENDEAVOUR),
24 Show a clean pair of heels (RUN FOR IT) to Bolt (bolt = RUN FOR IT),
25 Gene is out of grievances (‘gene’ is out of ‘grievances’ = rivacs = VICARS) with ministers (VICARS),
26 Sounds like (= homophone indicator) great craic (‘great craic’ = ‘great crack’ = BREAKAGE) as a consequence of smashing the record (BREAKAGE),
27 Back off (k) prior (prior/abbot = ‘monk’ without ‘k’ = MON-) to officer (Commanding Officer = -CO) following (= position indicator) a (-A-) (MONACO) French neighbour (MONACO).
Down:
1 Expresses relief (PRAISE BE) in Paris (Paris), excited (= anagram indicator) (Paris = PRAIS-) by drug (-E) from Belgium (BE) (PRAISE BE),
2 Mention (cite = -ETIC-) revolutionary (= reverse indicator) in Split (split/rent = R-ENT) (RETICENT) who wouldn’t say ‘boo’ to a goose? (wouldn’t say ‘boo’ to a goose = RETICENT),
3 Some fancy nickname (some ‘fanCY NICkname’ = CYNIC) for Cassandra (CYNIC),
5 To put it differently (IN OTHER WORDS), one (I-) is not (-N OT-) hot (-H-) on Queen (Elizabetha Regina = -ER) lyrics (WORDS) (IN OTHER WORDS),
6 Director’s workplace (film set/set = SE-T-) covers most of (t) the rent (‘rent’ without ‘t’ = -REN-), backing (= reverse indicator), for example (e.g. = -GE-), One (-I) (SERENGETI) African Grassland (SERENGETI),
7 Behind (IN DEBT) those who owe Bill (IN DEBT),
8 Network foundation (‘networK’ foundation = K-) on lough (Lough -ERNE-) and lake (-L) (KERNEL), in essence (essence/core = KERNEL),
11 Managing The Budget domestically (HOUSEKEEPING) with the Government refusing to hand over power presumably? (HOUSEKEEPING),
15 The Jam (traffic jam = ROADBLOCK) or The Police could be responsible for this and it annoys those in The Cars? (ROADBLOCK),
16 Nora (-NORA-) is overwhelmed by parents (PA-MA) (PANORAMA) with one view (PANORAMA),
17 Oriental (East = E-) state (= homophone indicator) plant (‘sow’ = ‘so’ = S-O) admits pressure (-PRESS-) (ESPRESSO) can be stimulating (ESPRESSO),
19 Sounds like (= homophone indicator) one of The Beatles (one of the ‘beatles’ = ‘beetle” = SCARAB) is lucky and charming perhaps (SCARAB is a lucky charm),
20 Is about to join The Union (FIANCÉ) working (= anagram indicator) in café (in café = FIANCÉ),
23 A friend in Havana (Spanish ‘friend’ = AMIGO) to some Miami government (some ‘miAMI GOvernment’ = AMIGO).