Across:
1 Pass (TICKET) Mark (TICK-) and Earl (-E-) going by car (model -T) (TICKET),
4 Time-outs (timeouts) travelling (= anagram indicator) (timeouts = TITMOUSE) with one of the tweeters (TITMOUSE = tit songbird),
9 What could be used to keep one of those Windsors in check? (TIEPIN for a Windors/tie) Open 22 across (open ‘tie in a bow’ = -TIE-) on the golf course! (-PIN) (TIEPIN),
10 Dump (TIP) beside institute (-I-) in urban area (town = TO W-N) (TIP TO WIN) – put your money on it to succeed in the Tidy Towns, for example (TIP TO WIN),
12 A number of muses (NINE-) at the start of 22 across (start of ‘tie in a bow’ = -TIE-) on the (the) Trim (e) (‘the’ without ‘e’ = -TH) (NINETIETH) granite, on an anniversary (granite anniversary = NINETIETH),
13 Barman (Attorney General = AG = -GA) is not (not) retiring (= reverse indicator) (not = TON-) (TONGA) to overseas foreign kingdom (TONGA),
14 Spike (TIP-) is on foot (-TOE) in the neighbourhood (AROUND) (TIPTOE AROUND) with creep, secretly (TIPTOE AROUND),
18 Airline would know the answer to this (TIME OF FLIGHT) measurement of how long it takes an object to travel (TIME OF FLIGHT),
21 It (it) gives rise (= reversal indicator) (it = TI-) to a (-A-) final number (final ‘numbeR’ = -R-) from a (-A) (TIARA) female band (TIARA),
22 Finish wrapping (TIE IN A BOW) it (it) up (= reverse indicator) (it = TI-) for a German (‘a’ German = ein = -E IN) /American (A) sounding (= homophone indicator) lover (‘beau’ = ‘BOW’) (TIE IN A BOW),
24 Unpromising letting gun off? (‘unpromising’ letting ‘gun’ off/without ‘gun’ = promisin = IMPRISON) Lock ’em up! (IMPRISON),
25 Persuasive type (COAXER) in company (CO-) chopper (chopper = -AXE-) over foundation (‘oveR’ foundation = -R) (COAXER),
26 Legendary female intellectual (TITANESS) working (= anagram indicator) in States (instates = TITANESS),
27 The Count (CENSUS) wants to know if you still believe in God? (CENSUS).
Down:
1 It (-IT-) is found in light brown (tan = T-AN-) pâté (pate) without foremost (p) (‘pâté’ without ‘p’ = -ATE) (TITANATE) salt (TITANATE),
2 They follow one disaster after another (CLEAN-UPS) or win big (CLEAN UP-) with tip on Shergar (tip on ‘Shergar’ = -S) (CLEAN-UPS),
3 Half a dozen (six) turning up (= reverse indicator) (six = -XIS-) in Alien (ET = E-T) (EXIST) survive (EXIST),
5 Flower (IRIS-) heads on hibiscus cut (heads on ‘Hibiscus Cut’ = -H C-) off (-OFF-) and cutback? (= reverse indicator) Look out for (see = -EES) (IRISH COFFEES) in local cocktails! (IRISH COFFEES),
6 Runner (MAT-) from Utah (-UT-) heading (f) off last (final) (‘final’ without ‘f’ = -INAL) (MATUTINAL) before noon (MATUTINAL),
7 A foreign (‘a’ foreign = UN-) type of Mistral (-WIND) (UNWIND) gets to slacken off (UNWIND),
8 Ruth comes out from underneath (‘Ruth’ comes out from ‘underneath’ = ndenea = ENNEAD) the nine of them? (a group of nine = ENNEAD),
11 Workers (MEN-) mellow (-AGE) on Artois (Artois) mixing (= anagram indicator) (Artois = A TROIS) (MENAGE A TROIS) with three people in nice Union accommodation? (Nice/French living together = MENAGE A TROIS),
15 Beastly type (OX-) is an idiot (an idiot) boss (= anagram indicator) (an idiot = -IDATION) (OXIDATION), – anyone working in the hairdressing industry will recognise this is a problem (OXIDATION),
16 Where do you think Humpty Dumpty and his family watch the play? (EGG BOXES) Where they’re holding the early birds! (EGG BOXES),
17 They have a job managing craft types (STEWARDS) of criminal (= anagram indicator) wasters (wasters = STEWAR-S) around Dublin (-D-) (STEWARDS),
19 Most (t) of the illusion (trick) (‘trick’ without ‘k’ = TRIC-) embraced by Stone (St = S-T) (STRICT) is of a harsh regime (STRICT),
20 React (react) badly (= anagram indicator) (react = CAR-ET) over pressure (-P-) (CARPET) from runner (CARPET),
23 Take her off one horse (take ‘her’ off ‘one horse’ = onose = NOOSE) – the type you can see from the gallows (NOOSE).