Across:
1 Old Persian leader (Shah) isn’t finished (h) (‘Shah’ without ‘h’ = SHA-) with guy (-MAN) (SHAMAN) who has a good knowledge of foreign spirits (SHAMAN),
4 Has nothing to do (IDLENESS) with why people won’t join Labour? (IDLENESS),
9 Annoying type (GADFLY) of grotesque, extreme (‘Grotesque’ extreme = G-) advertisement (-AD-) on Dart (dart/dash = -FLY) (GADFLY),
10 Going all the way back (= reversal indicator), Moor (moor/secure = tie = -E IT) from Spain (-E-) took relative (sis = -S I S-) to African summit (‘African’ summit = A-) (AS I SEE IT) for a personal opinion (AS I SEE IT),
12 For the present time (PARTY-), oddly (= anagram indicator) Gore (Gore = -GOER) (PARTYGOER) is the one celebrating (PARTYGOER),
13 Supporter of the art (EASEL) concealed by Achilles, Aeneas (concealed by ‘AchilLES AEneas’ = lesae) going all the way back (= reverse indicator) (lesae = EASEL),
14 Summer (SEASON) pass (TICKET) (SEASON TICKET) for one taking seat in The House over a prolonged period (SEASON TICKET),
18 For those who want to retire but can’t? (SLEEPING PILL) As for the rest, some will be put out by this! (SLEEPING PILL),
21 Rupert is out of plate armour (‘Rupert’ is out of ‘plate armour’ = laamo = ALAMO) for the mission that was under siege in Texas (ALAMO),
22 Has a job investigating (POLICEMAN) flower (flower/ River PO-) with parasitic insects (-LICE-) and half of those in 1 across (half of ‘shaMAN’ = -MAN) (POLICEMAN),
24 Rush (dart = TRAD-) back (= reversal indicator) to a foreign (a = ein = -E-IN-) school (-S) (TRADE-INS) in old cars (TRADE-INS),
25 Produced (= anagram indicator) a scent (a scent = STANCE) with attitude (STANCE),
26 Comfort (REASSURE) from Erasure’s (erasures) medley (= anagram indicator) (erasures = REASSURE)
27 Has no doubt (TRUSTS) this line is coming out of turnstiles (this ‘line’ is coming out of ‘turnstiles’ = tursts = TRUSTS).
Down:
1 It won’t lead someone astray (SIGNPOST) to endorse (SIGN-) picket (picket/wooden stake = -POST) (SIGNPOST),
2 Area (A-) let initially (‘Let’ initially = -L-) to the foreign (‘the’ German = -DER-) chap (-MAN) (ALDERMAN) on the English council (ALDERMAN),
3 Tortes from tea trolleys (‘tortes’ from ‘tea trolleys’ = eally = ALLEY) in a narrow passageway (ALLEY),
5 The little pig’s house of straw presumably (DESTRUCTIBLE) is not made to last (DESTRUCTIBLE)
6 Seasonal gift (EASTER EGG) produced by awkward (= anagram indicator) eaters (eaters = EASTER), for example (e.g. = -EG-), is great (-G) (EASTER EGG),
7 Trial comes out of revelations (‘trial’ comes out of ‘revelations’ = eveons = EVEN SO) nevertheless (EVEN SO),
8 Come to terms (SETTLE) with telecaster not taking care (‘telecaster’ not taking ‘ care’ = telest = SETTLE),
11 Courage, locally (‘courage’ locally = BOTTLE), to get Frank (OPEN-) Ward (-ER) (BOTTLE OPENER) a Swiss army knife (BOTTLE OPENER),
15 The Observer’s (the observers = ONLOOKERS) people with a view (ONLOOKERS),
16 Made (made) up (= reverse indicator) reports (= homophone indicator) (‘made’ = ‘maid’ = DIAM-) for broadcasting (broadcasting = -ON-) by detective (DS = -DS) (DIAMONDS) misappropriated by jewel thieves (DIAMONDS),
17 Switches (= reverse indicator) pepper (cayenne pepper = KN = -NK-) in table’s (tables) mill (= anagram indicator) (tables = BLA-ETS) (BLANKETS) for covers (BLANKETS),
19 Opens 6 down (opens ‘Easter egg’ = EASTER) with a spring annual that follows some hard and fast rules (EASTER follows Lent),
20 Costa Rican neighbour (PANAMA), a (-A) worker (man = -NAM-) from press agency (Associated Press = PA-), retires completely (= reverse all letters) (PANAMA),
23 Educator releases duo (‘educator’ releases ‘duo’ = ecatr = CATER) to provide party food (CATER).