Across
1 Dour (dreary) around (Housing) ET (alien as in extra terrestrial) = detour = circuitous route
4 CID (British cops) in anagram (terrible) of “state” = acid test = definitive trial
9 Au (gold) + par (standard) around (introduced to) I = au pair = foreign worker
10 Budge (compromise compared with not budging) in ONT (initial letters of Offering New Terms) = on budget = no cost over-run
12 Leaves are out in spring; leaves out = misses (as in omits)
13 Lego (brick company) around t (time) = let go = fire
14 Anagram (mess) of “that wastrel’s) = the last straw
18 Anagram (wnadering) of “near Shetland” = Neandethals = people who no longer exist
21 WOund = tightened; bound = spring; removing b (top) and adding W (weight) makes bound into wound
22 Outwit (trick) + hit (shot) = out with it = tell us what happened
24 Baguette (food from France) sounds like (picked up) bagette i.e. a little bag
25 Beggar (challenge as in beggar belief) = bear (hold as in hold responsibility) + gg (horse) inside
26 Trying = testing + h from ‘hard’, absorbed (anagram) = The Sting, a film
27 Pick (select) and nick (cut) sounds like picnic = outdooor meal
Down
1 Dead and late are two synonyms of passed = well behind
2 Anagram (transformed) = “tap water” = readily available liquid
3 Couple = unite, contained and reversed (held up) in disquiET IN University
5 Constituents are what something is made up of; it also means people a politician looks after
6 Do (act) x 2 = double act = a comic turn
7 Height (maxumum i.e. the height of luxury); if the h (the first letter) moves to be the last = eighth = 12.5%
8 Oot (Scots dialect for out) reversed (turn) = too with tat (rubbish) before it = tattoo = display (e.g. the Edinburgh Tattoo)
11 Rooting (cheering) and tooting ( = horn blowing) without last letters = Rootin’ Tootin’ = US expression for boisterous
15 Odd letters of AuDiT = adt; insert two men+ aMENdMENt = change
16 Path (approach) + o (zero) + gen (information) = pathogen = cause of disease
17 Anagram (melted) of “ice store” = esoteric = secret
19 Two (brace) + bit (took hold) = two bit = not important
20 Burgle (knock over as in knock over a house) = bugle (instrument) round (holding) r (first letter of rehearsals)
23 Even letters (regularly) of sEeN inside (being entertained by) ici (French for here) = Iceni, an old British tribe