ACROSS
1 Vessel has slate on lip (8)
SAUCEPAN – PAN [slate] on SAUCE [lip]
5 Settle down in Arsenal’s opening match (6)
ALIGHT – A{rsenal} + LIGHT [match]
9 Calm down, please: official’s inside (4,3)
EASE OFF – hidden in {pl}EASE OFF{icial}
14 Modish poem contains a line on worker, perhaps without style (11)
INELEGANTLY – IN ELEGY [modish | poem] contains L [a line] on ANT [worker, perhaps]
15 Doctor knocked back drink, once again dispatched everywhere (11)
OMNIPRESENT – reversed M.O. [doctor] + NIP RE-SENT [drink | once again dispatched]
16 Confidence bound to be picked up (5)
TRUST – homophone of TRUSSED [bound]
17 Clouds having been formed containing radioactive element, note (7)
NEBULAE – (BEEN*) [“formed”] containing U LA [radioactive element | note]
18 Novel with fantastic genre to flog in bulletin (9)
NEWSFLASH – NEW [novel] with SF [fantastic genre] + LASH [to flog]
19 Abnormal sort of water in Derwent’s banks (7)
DEVIANT – EVIAN [sort of water] in D{erwen}T
20 Send on deployment of troops, say, following Thirty Years War? (4-11)
POST-REFORMATION – POST RE FORMATION [send | on | deployment of troops, say]
22 Used to give support, at first (6-4)
SECOND-HAND – HAND [to give], SECOND [support] at first
23 Depict resistance fighters on edge, retreating (6)
MIRROR – R O.R. [resistance | fighters] on reversed RIM [edge]
25 Condescend to listen to EU citizen (4)
DANE – homophone of DEIGN [condescend]
28 Crazy whirl upstaging enchanting event? (9,5)
WALPURGIS NIGHT – (WHIRL UPSTAGING*) [“crazy”]
30 A lot of craft to satisfy a welcoming crowd (8)
FLOTILLA – FILL A [to satisfy | a] “welcoming” LOT [crowd]
32 Venomous man, a day tripper (8)
ACIDHEAD – ACID HE A D [venomous | man | a | day]
34 Hinder false advertiser, one offering advice (4-4,6)
BACK-SEAT DRIVER – BACK [hinder (as in, more hind)] + (ADVERTISER*) [“false”]
37 Make unclear, short publicity text (4)
BLUR – BLUR{b} [“short” publicity text]
38 Heartless fool screening film in old age (6)
NINETY – NI{n}NY [“heartless” fool] “screening” E.T. [film]
39 Admitting depression, crooks joining church recover (10)
CONVALESCE – “admitting” VALE [depression], CONS [crookes] joining CE [church]
43 Subject promises to settle coastal area, being quarrelsome (15)
CONTENTIOUSNESS – CONTENT IOU’S NESS [subject | promises to settle | coastal area]
45 Vain Englishman and American crossing river (7)
POMPOUS – POM [Englishman] and U.S. [American] “crossing” PO [river]
47 Mobile phone with charm and a reluctance to innovate? (9)
NEOPHOBIA – (PHONE*) [“mobile”] with OBI [charm] and A
49 Agreement to embrace John? Nothing is impossible (2,3,2)
NO CAN DO – NOD [agreement] to “embrace” CAN [john] + O [nothing]
51 Crustacean luckily protecting back bones (5)
ULNAE – hidden reversed in {crustac}EAN LU{ckily}
52 It’s almost the end in sentence (4,7)
HOME STRETCH – HOME [in] + STRETCH [sentence]
53 The writer’s to offer books without forethought (11)
IMPROVIDENT – I’M PROVIDE NT [the writer’s | to offer | books]
54 Singular art including most blue (7)
SADDEST – S [singular] + ADDEST [(thou) art including]
55 Person managing to seize one unoriginal type (6)
COPIER – COPER [person managing] to “seize” I [one]
56 Kid by cool water experiencing heat (2,6)
IN SEASON – SON [kid] by IN SEA [cool | water]
DOWN
1 Awkward son went off the straight and narrow (7)
STILTED – S TILTED [son | went off the straight and narrow]
2 A French ass, say, mostly loud and clear (11)
UNEQUIVOCAL – UN [a French] + EQUI{d} [ass, say, “mostly”] + VOCAL [loud]
3 Reader’s issue with English agreed by school (9)
EYESTRAIN – E YES [English | agreed] by TRAIN [school]
4 Unnatural profit, in a way, with vodka and beer? (7,3,5)
AGAINST THE GRAIN – GAIN [profit] in A ST [a | way] with THE GRAIN [vodka and beer (as opposed to THE GRAPE]
6 No republican initially changing sides? He won’t (8)
LOYALIST – ROYALIST [no republican], changing his initial letter from R(ight) to L(eft), and becoming someone who won’t change sides, in a semi-&lit kind of way.
7 Blooming head of theatre and choir take off (5,9)
GLOBE ARTICHOKE – GLOBE [theatre] + (CHOIR TAKE*) [“off”]
8 It helps musician to grin, with funk playing (6,4)
TUNING FORK – (TO GRIN + FUNK*) [“playing”]
9 Entitle army corps to pull back holding detainee (7)
EMPOWER – reversed REME [army corps] holding POW [detainee]
10 Note what’s up in the papers? (5)
SHEAF – reverse all of FA EH’S [note | what’s]
11 Frank, mostly sensible, is running (11)
OPERATIONAL – OPE{n} RATIONAL [frank, “mostly” | sensible]
12 Pretty female making an impression (8)
FETCHING – F ETCHING [female | making an impression]
13 Go crazy, in a spin (4)
STAB – reversed BATS [crazy]
20 Castigate attempt at humour, to a degree (6)
PUNISH – PUN ISH [attempt at humour | to a degree]
21 Go off northwards after car, I hear (7)
AUDITOR – reversed ROT [go off] after AUDI [car]
22 I’m not interested in female item of clothing (2,4)
SO WHAT – SOW HAT [female | item of clothing]
24 Maybe what could make inventor pour ale (8,7)
RELATIVE PRONOUN – (INVENTOR POUR ALE*) [“could make…”]
26 Inclusive approach gets old man aboard Britain’s new vessel (14)
BIPARTISANSHIP – PA [old man] “aboard” (BRITAIN’S*) [“new”] + SHIP [vessel]
27 Children’s writer‘s block has no end (6)
BARRIE – BARRIE{r} [block “has no end”]
29 Throw up, at first, on new drug (7)
UNHORSE – U{p} on N HORSE [new | drug]
31 Goddess, we’re told, is like a carrier of blood (6)
VENOUS – homophone of VENUS [goddess]
33 One learner guided around in class is ignorant (3-8)
ILL-INFORMED – I L LED [one | learner | guided] around IN FORM [in | class]
35 Loveless letters penned by thick aristocrat (11)
VISCOUNTESS – N{o}TES [“loveless” letters] “penned” by VISCOUS [thick]
36 Pragmatic criminal in court takes fellow in (10)
UNROMANTIC – (IN COURT*) [“criminal”] takes MAN [fellow] in
40 Echo behind cattle car (9)
LIMOUSINE – E [Echo] behind LIMOUSIN [cattle]
41 Kind of leaves a prison in this way (8)
ACANTHUS – A CAN THUS [a | prison | in this way]
42 Responding with original, moving chapter (8)
REACTIVE – CREATIVE [original], moving its C [chapter] to a different place in the word
44 Not dressed in rubbish fabric (7)
TABARET – BARE [not dressed] in TAT [rubbish]
46 Two versions of small figure to placate (7)
SWEETEN – S WEE [two versions of small] + TEN [figure]
48 Eats meal briefly, in rush (5)
HASTE – HAS TE{a} [eats meal “briefly”]
50 Regularly in toupee? You must be joking (4)
NOPE – {i}N {t}O{u}P{e}E{e}
WALPURGIS NIGHT has come up before a couple of times, or I wouldn’t have had a clue.
Yes, my LOI was ‘acidhead’/’unhorse’, but they weren’t that difficult with the checkers in place.
Time: long.
Minor typo: your clue of the day is 34across (not down).