Across:
1 Album (RECORD) by New (= anagram indicator) Order (order = RE-ORD) includes first cover (first ‘Cover’ = -C-) (RECORD),
4 A winger’s (a wingers) shot (= anagram indicator) (a wingers = SWEARING) is promising (SWEARING),
9 Kill (slay) report (= homophone indicator) (‘slay’ = ‘SLEIGH’) – the one on the house at Christmas (SLEIGH),
10 Bad start (‘Bad’ start = B-) to be without (-LACK) most of the (m) players? (‘team’ without ‘m’ = TEA) (BLACK TEA) Swallow it without milking it! (BLACK TEA),
12 Clare (-CE-) pub (BAR-) opens (= positional indicator) with free (= anagram indicator) loan (loan = -LONA) (BARCELONA) of Iberian port? (BARCELONA),
13 Eurosceptic dismisses Cicero (‘eurosceptic’ dismisses ‘Cicero’ = euspt = UPSET) as pushover? (push/knock over = UPSET),
14 Blow (SOUND) the consequences (EFFECTS) (SOUND EFFECTS), as they’re responsible for creating noise and making a scene (SOUND EFFECTS),
18 It’s how The Count met his maker (Dracula died with stake through heart = BORED TO DEATH) in time for something new (BORED) for half the town (half the ‘town’ = TO) and most of those in 27 across (most of ‘deaths’ = DEATH) (BORED TO DEATH),
21 In retrospect (= reversal indicator), model (model = pose = -ESOP) on first assignment (first ‘Assignment’ = A-) (AESOP) told tales about morality in the past (AESOP),
22 Place in the Church (altar) State (= homophone indicator) (‘altar’= ‘ALTER’) for big heads (EGOS) (ALTER EGOS) or other personalities (ALTER EGOS),
24 Slowly but surely (STEADILY) it delays (it delays) change (= anagram indicator) (it delays = STEADILY),
25 Unapologetic dropping Piaget (‘unapologetic’ dropping ‘Piaget’ = unoloc = UNCOOL) – it’s not acceptable (UNCOOL),
26 Form of Marxism (LENINISM) produced by OAP from Minneapolis (‘OAP’ from ‘Minneapolis’ = minnelis = LENINISM),
27 Headstone doesn’t include one (‘headstone’ doesn’t include ‘one’ = headst = DEATHS) of a number of fatalities (DEATHS).
Down:
1 Mother of Kennedy (ROSE- Kennedy), the American president (George Bush = -BUSH), (ROSEBUSH) found in the garden of the White House (ROSEBUSH found in The White House’s rose garden),
2 Positive (CHEERFUL) applause (CHEER-) for beating (= anagram indicator) flu (flu = -FUL) (CHEERFUL),
3 Valet leaves travelogue (‘valet’ leaves ‘travelogue’ = rogue = ROGUE) in a bad state (ROGUE state),
5 Dole (WELFARE) from Kansas (STATE) (WELFARE STATE) has a reputation for helping the less prosperous in society (WELFARE STATE),
6 Story (ACCOUNT-) editor (-ED) (ACCOUNTED) backed up report (ACCOUNTED for),
7 The first person (I) with quality heading (‘Quality’ heading = Q) for trial (TEST) (IQ TEST) with talent spotter (IQ TEST),
8 Research aid (GRANTS) for half (half) the food (grub) (half the ‘GRub’ = GR-) workers (-ANTS) (GRANTS),
11 Firm (CO-) is first to fundamentally (first to ‘Fundamentally’ = -F-) charge (-FEE) for showing position of the various competing teams (TABLES) (COFFEE TABLES) to supporters of the various cups (COFFEE TABLES),
15 Went to see (DROPPED IN) doctor (DR-) for small surgical procedure (operation = -OP-) to do with head pain (head ‘Pain’ = -P-) – medic (medic) at centre (edi) (‘mEDIc’ at centre = -ED I-) is initially nonplussed (initially ‘Nonplussed’ = -N) (DROPPED IN),
16 Haunts (HANGS OUT) pin-up (HANG) introducing songs (introducing ‘Songs’ = -S) on holiday (OUT) (HANGS OUT),
17 Shtetl is (shtetl is) built (= anagram indicator) (shtetl is = THISTLES) by prickly types from the meadow (THISTLES),
19 Beanie sports one (beanie hat has a TASSEL) at The Fringe (fringe/bobble = TASSEL),
20 Relative of Daisy’s (ASTER-) not the first (‘Not’ the first = -N) (ASTERN) back from the navy? (‘back’ from the navy? = ASTERN),
23 Class (RANGE) of Orangeman ignoring moan (‘Orangeman’ ignoring ‘moan’ = rgean = RANGE).