Across:
1 Petition to get the hell out of dodge? (APPLY FOR LEAVE) Give me a break! (APPLY FOR LEAVE),
10 Call yours truly (PHONE ME) in gym (PE = P- E-) about perfect (-HONE-) start to morning (start to ‘Morning’ = -M-) (PHONE ME),
11 Gets the message (WISES UP) from Workers Party (WP = W- -P) over potential (= anagram indicator) issue (issue = -ISES U-) (WISES UP),
12 Literally releases alert (‘literally’ releases ‘alert’ = lily = LILY) of a symbol of Easter (LILY),
13 Source (START) for close friends (close/end ‘friendS’ = -S-), a flavour of The Cranberries (-TART) (START),
15 Suspension (LULL) of three students (3 learners = 3 x Ls = L-LL) around university (-U-) (LULL),
17 Copy (copy/ape = APE) produced by the environmentalists (Environmental Protection Agency = EPA) doing a U-turn (= reverse indicator) (EPA = APE),
19 Shortage of grub (FAMINE) in (-IN-) celebrity (FAM-E) enclosure (FAMINE)
21 Once in a blue moon (RARELY) ace is out of relay race (‘ace’ is out of ‘relay race’ = relyra = RARELY),
22 Under par (ILL-) and leading invitational (leading ‘Invitational’ = -I-) briefly (e) – single out for praise (cite) (‘cite’ without ‘e’ = -CIT) (ILLICIT) or is that forbidden? (ILLICIT),
23 Bootleg tape (RIP-OFF) of jazz lick (riff = RI-FF) entertains President (-P-) Obama from the start (‘Obama’ from the start = -O-) (RIP-OFF),
25 Old city (-UR-) in Belgium (BE = B-E-) with gold (-AU) (BUREAU) agency (BUREAU),
27 One of the Seven Dwarfs (DOC) saw bones locally? (sawbones ‘locally’ = doctor or surgeon = DOC),
29 Section of sweet alyssums (section of ‘sweET ALyssums’ = etal) dug up (= reverse indicator) (etal = LATE) could be dead (LATE),
30 Posts from test pilots (‘posts’ from ‘test pilots’ = tetil = TITLE) – indeed? (TITLE in deed),
31 Swear (CUSS) in primary candidate (primary ‘Candidate’ = C-) from America (-US-) to open summit (open ‘Summit’ = -S) (CUSS),
34 Uncle’s mate (aunt) talking (= homophone indicator) (‘aunt’ = ‘ant’ = ANT) to those in 32 down (‘hill’ = -HILL) (ANTHILL) from The Queen’s residence? (ANTHILL),
35 Hamilton (capital of Bermuda = CAPITAL) or Washington? (CAPITAL of United States of America),
36 Twist someone’s arm (APPLY PRESSURE) to stop the bleeding? (APPLY PRESSURE).
Down:
2 Poser (PROBLEM) is a pain in the neck locally (PROBLEM),
3 Red herrings (LIES) in light waves on the banks (‘LIght wavES’ on the banks = LIES),
4 Included in selfie staggering (included in ‘selFIE STAggering’ = FIESTA) out of Spanish celebration (FIESTA),
5 Water skier disregards task (‘water skier’ disregards ‘task’ = werier = REWIRE) to hook-up the cable again (REWIRE),
6 Guide slowly (EASE) eating like a horse? Only the sides! (‘EAting like a horSE’ only the sides = EASE),
7 Type of dress you’d associate with the poets (VESTURE) in Utah (UT) raised (= reverse indicator) (UT = -TU-) in free (= anagram indicator) verse (verse = VES-RE) (VESTURE),
8 Take advantage of one’s credit rating (APPLY FOR A LOAN) and make a request to a person who takes interest in their work (APPLY FOR A LOAN),
9 Pay attention (APPLY YOURSELF), as this might be advice to summit a curriculum vitae (APPLY YOURSELF),
14 Tropical fruit (ARPICOT) in starter of Arborio (starter of ‘Arborio’ = A-) rice (rice) mostly (e) (‘rice without ‘e’ = -RIC-) consumed by Kitty (kitty/pot = -P-OT) (APRICOT),
16 Cocktail (‘cocK’ tail = K-) is fine (fine) – possibly (= anagram indicator) (fine = -NIFE) (KNIFE) it will take the edge off (KNIFE),
18 Stopped lying (SAT UP) to Deb from Budapest (‘Deb’ from ‘Budapest’ = uapst = SAT UP),
20 Content of caramel-free (content of ‘caramEL Free’ = ELF) spirit (ELF),
21 Kid (kid/tease = RIB) raised (= reversal indicator) in Novosibirsk (in ‘novosiBIRsk; = bir = RIB),
24 Stakes (stakes = pots) – a favourite of the gamblers (tip) all backing (= reverse all indicator) (pots = STOP + tip = PIT) (PIT STOP) off the track with the rest? (PIT STOP),
26 Peer (equal) briefly (l) (‘equal’ without ‘l’ = EQUA-) takes to (-TO-) writing (from the 3Rs = -R) (EQUATOR) to one with no latitude? (EQUATOR),
27 Retired (= reverse indicator), from a financial perspective? Settled (paid = DIA-P) around university (University of Limerick = UL = L-U-) (DIAL-UP) with an outdated connection! (DIAL-UP),
28 Sounds like (= homophone indicator) lake (‘lough’ = ‘loch’ = -LOCH-) in Clare (C-E) (CLOCHE) offers protection to those in the plot (CLOCHE),
32 High explosive shell found on the borders of (‘HIgh explosive sheLL’ found on the borders = HILL) of Dublin terrace (HILL at Croke Park),
33 Some characters develop useful (some characters ‘develOP USeful’ = OPUS) work by the artist (OPUS).