Across:
1 Playing away from home (FOOLING AROUND) putting on an act (FOOLING) for a (A-) few drinks from the bar (-ROUND) (FOOLING AROUND),
10 On holiday (OUT-), fiction (-LIE-) is read primarily (‘Read’ primarily = -R) (OUTLIER) by detached person (OUTLIER),
11 Don’t obsess over (LET IT GO) Tweeter (tit = -T IT) taken in by Scandi building firm (Lego = LE- GO) (LET IT GO),
12 Backing (= reversal indicator) track (rail = LIAR) tells a story but not necessarily the right one (LIAR),
13 Kids (FOOLS) kind of popular with all sides today (‘fool’ on all sides of today’s grid / FOOLS),
15 Put one over on (FOOL) most of those in 13 across (most ‘fools’ = FOOL),
17 Tiny bit (WEE) served up (= reversal indicator) in slice of crème brûlée waffle (in slice of ‘crème brûlée waffle’ = eew = WEE),
19 Recognition (CREDIT) for Direct (direct = CREDIT) Action (= anagram indicator),
21 House of Lords leader’s (‘House Of Lords’ leaders = HOL-) party (Democratic Unionist Party = -D-UP) (HOLD-UP) offering to delay (HOLD-UP),
22 Do a job in The Station (do a job in the TV/Radio station = AIR SHOW) for one of those crafty types making a spectacle in Sky (AIR SHOW),
23 Like one of those in 31 across (‘bird’ = PIGEON) from The Messenger (PIGEON),
25 Journalist (EDITOR) has a job managing what’s found at the end of 8 down (EDITOR manages ‘foolscap paper’),
27 Some nerve tissue (some ‘nerVE Tissue’ = VET) from old hand (old hand/veteran = VET),
29 Tools for punching holes (AWLS) in walnuts to remove nut (‘walnuts’ to remove ‘nut’ = wals = AWLS),
30 Touchy sort of royal (King MIDAS – ‘the midas touch’) has cranky (= anagram indicator) maids (maids = MIDAS),
31 Take capers off crispbread (take ‘capers’ off ‘crispbread’ = ribd = BIRD) to swallow (BIRD),
34 Sex-up (ENLIVEN) last correspondence (last ‘correspondencE’ = E-) by Lenin (Lenin = -NLI-EN) mysteriously (= anagram indicator) about victory (-V-) (ENLIVEN),
35 Captains on the boats (skippers) need no introduction (s) (‘skippers’ without ‘s’ = KIPPERS) to the fish (KIPPERS),
36 Reckless behaviour (FOOLHARDINESS) of clowns (FOOL-S) welcoming Sheridan (Sheridan = HARDINES-) adaptation (= anagram indicator) (FOOLHARDINESS).
Down:
2 Exposed (OUT-) passion (-RAGE) (OUTRAGE) leads to scandal (OUTRAGE),
3 Set down (LAID down) area (-A-) in covering (L-ID) (LAID),
4 Not the first (‘Not’ the first = N-) to lose the head (y) with Herb (‘yarrow’ = -ARROW) (NARROW) in a tight space (NARROW),
5 A type of gene (ALLELE) produced by everybody (ALL-) lost (-L-) in drugs (= -E-E) (ALLELE),
6 Guarantee (OATH) offers assurances to leader’s (“Offers Assurances To” leaders = OAT-) husband (-H) (OATH),
7 One of those things you’d see in court (NET CORD in tennis court) or catch (NET) on tape (CORD) (NET CORD),
8 The writer possibly wrote the book on (FOOLSCAP PAPER) jokers (jokers = FOOLS) from The Crown (crown = =CAP) taking exam (PAPER) (FOOLSCAP PAPER),
9 The Blockheads (fools = FOOL’S) and Nirvana (PARADISE) (FOOL’S PARADISE) produced in blissfully ignored State (FOOL’S PARADISE),
14 Showing strength in field (strength of the magnetic field = OERSTED), some South Africans (Boers) lose the head (b) (‘boers’ without ‘b’ = OERS-) with the (the) gutless (h) (‘the’ without ‘h’ = -TE-) department (-D) (OERSTED),
16 Sorting out of waiting rooms (‘sorting’ out of ‘waiting rooms’ = waiom = MIAOW) is Tom’s call (MIAOW),
18 Jones’ partner (DOW- Jones) is heartless (r), cynical, in a manner of speaking (‘dry’ without ‘r’ = -DY) (DOWDY), and not smart (frumpy = DOWDY),
20 In retrospect (= reversal indicator), it’s similar to 15 across (similar to ‘fool’ = nit = TIN) in The Can (TIN),
21 Ground-breaking type (HOE) of starters on heavy oil engines (starters on ‘Heavy Oil Engines’ = HOE),
24 Scientist associated with Sky (GALILEO) had problems with The Sun’s direction perhaps (GALILEO),
26 Picked up in the gym (TRICEPS) for getaways (trips = TRI-PS) around Clare (-CE-) (TRICEPS),
27 Anne VI (Anne VI = VIENNA) lost (= anagram indicator) European capital (VIENNA),
28 Spilled the beans on (TALKED) stakeholders getting rid of horses (‘stakeholders’ getting rid of ‘horses’ = taklde = TALKED),
32 Guys from Yugoslav (‘guys’ from ‘Yugoslav’ = olav = OVAL) sports stadium (OVAL),
33 Frank (OPEN) Cook? (= anagram indicator) Nope! (nope = OPEN).