Across:
1 Daisy’s relative (-ASTER) is following (= positional indicator) loud music (forte = F-) (FASTER) that’s got a quicker tempo (FASTER),
4 Kitty (puss = S-S UP) goes back (= reversal indicator) around lake (-L-) with frozen water (-ICE-) (SLICES UP) in sections (SLICES UP),
9 Had another look at (REREAD) grenadier spitting out gin (‘grenadier’ spitting out ‘gin’ = reader = REREAD),
10 Criminal (= anagram indicator) stole cab (stole cab = OBSTACLE) by barrier (OBSTACLE)
12 Sends up (= reversal indicator) Ross (Ross = -SSOR) on a horse (-GG-) in the 20s, for example (era = A-RE-) (AGGRESSOR), taking the fight to others (AGGRESSOR),
13 Bowl over (AMAZE) with a (A-) type of cereal (maize) that’s empty? (empty/remove middle letter = i) (‘maize’ without ‘i’ =-MAZE) (AMAZE),
14 Take hold of (AFFECT-) toe in a (toe in a = -IONATE) shower (= anagram indicator) (AFFECTIONATE) in a touchy-feely sort of way (AFFECTIONATE),
18 Link (ATTACH-) to sick people (cases) on the Internet perhaps (e-cases = -E CASES) (ATTACHE CASES) being carried out of the embassy (ATTACHE CASES),
21 In mythology, The Messenger (goddess IRIS-, messenger of the gods), Hacketstown Leader (‘Hacketstown’ leader = -H) (IRISH) and The Clare People (IRISH),
22 Clean hands (INNOCENCE) – you can’t be prosecuted for that! (INNOCENCE),
24 English (E-) movement’s (movements = -MOTIONS) (EMOTIONS) strong feelings (EMOTIONS),
25 Pleasant smells (AROMAS) from a (A-) chipper (-ROMA-) at top of the Strand (top of the ‘Strand’ = -S) (AROMAS),
26 Kitty (kitty/pool of money = POT-) on the bike? (-BELL-) Yes (-Y) (POTBELLY), with spare tyre! (POTBELLY),
27 Picking up the readings (SENSOR) of Nabokov initially (‘Nabokov’ initially = -N-) in Roses, (Roses = SE-SOR) going all the way back (= reversal indicator) (SENSOR).
Down:
1 Shoot (FIRE AWAY) at the end of 15 down (‘catch fire’ = FIRE) is missing from The Office (AWAY) (FIRE AWAY),
2 Take no notice of (SHRUG OFF) indifferent gesture (SHRUG) on holiday (OFF) (SHRUG OFF),
3 Put a line through (ERASE) some disclaimer as expected (some ‘disclaimer as expected’ = er as e = ERASE),
5 Describes The Maze (LABYRINTHINE) complex (LABYRINTHINE),
6 Member of old heretical sect (CATHAR-) finds time (-T-) in charge (in charge = -IC) (CATHARTIC) is a relief (CATHARTIC),
7 What was the function (SOCIAL) of The Gathering? (SOCIAL),
8 Peter’s (peters = PRESET) treatment (= anagram indicator) is arranged in advance (PRESET),
11 A (A-) Pole (South Pole = -S-) working as a detective (private investigator = -PI-) has reasonable (-RATIONAL) (ASPIRATIONAL) character of one who wants to be successful (ASPIRATIONAL),
15 Light (CATCH FIRE) to take prisoner by surprise (CATCH) opening 19 down (“fire up” = FIRE) (CATCH FIRE),
16 Opening the (opening ‘the’ = T-) paper (-SUN-) to Parisian friends (Parisian/French ‘friends’ = ‘amis’ = -AMIS) (TSUNAMIS) causes waves of disturbances (TSUNAMIS),
17 Fool (ASS-) showing off (= anagram indicator) roses (roses = -ESSOR) (ASSESSOR) in The Examiner (ASSESSOR),
19 Most of (r) the Irishmen (Irish ‘men’ = ‘Fir’ without ‘r’ = FI-) going to Peru (Peru = -RE UP) unexpectedly (= anagram indicator) (FIRE UP) stir the imagination (FIRE UP),
20 Doctor (doctor/tamper = RIG-) is not in office (-OUT) (RIGOUT) uniform (RIGOUT),
23 College (C-) pool (purse) fails to open (p) (‘purse‘ without ‘p’ = -URSE) (CURSE) for a spell (CURSE).