Across:
1 Cover old ground (REHASH) around (= reverse indicator) those looking after safety (HSA = -ASH) for that woman (her = REH-) (REHASH),
4 People from Spain and Portugal (IBERIANS) and Serbia in (Serbia in) trouble (= anagram indicator) (Serbia in = IBERIANS),
9 Mediterranean (SEA) boxer (DOG) (SEA DOG) – presumably, Long John Silver’s best friend, in a manly way? (man’s best friend/pirate’s best friend = SEA DOG),
10 Archaeologist’s discoveries (FIND-S) include interpreting neoclassical gold heads (‘Interpreting Neoclassical Gold’ heads = -ING) (FINDINGS) – the ones the researchers came up with (FINDINGS),
12 Getting better (ON THE MEND) broadcast (ON) by The Others (them = THE M-) for finale (-END) (ON THE MEND),
13 In a frenzy (IRATE), buccaneer (pirate) loses the head (p) (‘pirate’ loses ‘p’ = IRATE),
14 Starts 18 across (starts ‘self-employed’ = SELF-) with appeal (INTEREST) (SELF-INTEREST) that’s a concern to me (SELF-INTEREST),
18 Has a job minding one’s own business (SELF-EMPLOYED) in Labour – for one, not being part of the general staff (SELF-EMPLOYED),
21 Bit of The Paper illustrating (bit of ‘the paPER ILlustrating’ = PERIL) danger (PERIL)
22 Oriental (East = E-) leaders in Mongolia (leaders ‘In Mongolia’ = -IM-) in firm (stable = -ST-ABLE) (ESTIMABLE) worthy of great respect (ESTIMABLE),
24 Steer a course (NAVIGATE) for vain (vain) criminal (= anagram indicator) (vain = NAVI-) – the one standing alongside The Fence (-GATE) (NAVIGATE),
25 A wise woman (ATHENA) back in the day (-THEN-) in teetotal organisation (AA = A-A) (ATHENA),
26 Display stands (open shelves = ETAGERES) for reviewing (= reverse indicator) view (see = -E-ES) across river (-R-) to theatre (Gate = -ETAG-) (ETAGERES),
27 Throwaway lines (ASIDES) from The Undertones on stage (ASIDES).
Down:
1 Press one (press one) criminal (= anagram indicator) (press one = RESPONSE) to answer (RESPONSE),
2 Early hit (early hit) played (= anagram indicator) (early hit = HEARTILY) with enthusiasm (HEARTILY),
3 Hurting (sore = S-ORE) over model (model -T-) (STORE) in boutique (boutique/shop = STORE),
5 Homemaker’s (BUILDER’S) partner (MATE) (BUILDER’S MATE) is helping one of those doing the housework (BUILDER’S MATE),
6 Director (-D) passes away (DIES-) in film unit (reel = RE- -EL) (RED DIESEL) fuelling growing concerns? (RED DIESEL = fuel for farmers),
7 Once a year (ANNUAL) idealists leave Aleutian Islands (‘idealists’ leave ‘ Aleutian Islands’ = uanlan = ANNUAL),
8 Method (SYSTEM) to sympathisers with no parish (‘sympathisers’ with no ‘ parish’ = symtes = SYSTEM),
11 In the house, for instance, pink (LEFT-OF-CENTRE) port (LEFT-) to go with starters, oysters fish (starters ‘Oysters Fish’ = OF) and recent (recent) bake (= anagram indicator) (recent = CENTRE) (LEFT-OF-CENTRE),
15 Dogmatist (IDEOLOGUE) with loud ego (loud ego) working (anagram indicator) (loud ego = -DEOLOGU-) in Ireland (.ie = I-E) (IDEOLOGUE),
16 Type of whiskey (RYE whiskey) bishop (B-) takes to study (-READ) (RYE BREAD) – presumably it can be used for toast? (RYE BREAD),
17 Journalist (ED-), for example (e.g. = -GE-), takes up (= reverse indicator) techniques (-WAYS) (EDGEWAYS) of how to get a word in? (EDGEWAYS),
19 Key (music key -G-) found in building (= anagram indicator) opens (opens = SPON-E) (SPONGE) one of those in the bakery (SPONGE),
20 Log in leaving invigilator (‘log in’ leaving ‘invigilator’ = iviatr = TRIVIA) the unimportant facts (TRIVIA),
23 Those on board (those on board ship = MATES) closing 5 down (closing ‘builders mate’ = MATE-) and school (-S) (MATES).