Across
First to abandon lots of work demands (4)
I haven't cracked this one yet — but Times for the Times have:
TASKS = lots of work, lose the T.
Old Andeans only in touch with European for insurance? (4,2,4)
I haven't cracked this one yet — but Times for the Times have:
JUST (only) INCAS (old Andeans) E(uropean).
Obsession shown in hunting bird with cavalry (10)
Donkey's stealing heart from governess Grey (4)
I haven't cracked this one yet — but Times for the Times have:
AGNES Grey being the eponymous governess in Anne Bronté’s novel, lose her central N to get AGES, as in donkey’s years.
Gained an advantage, committed to staff (6)
Elected, given ample time for U-turn as necessary (8)
I haven't cracked this one yet — but Times for the Times have:
IN (elected) then LARGE T all reversed.
An educationalist retired? (4)
I haven't cracked this one yet — but Times for the Times have:
A Bachelor of Education, B.Ed.
English bully arrives outside port fighting activist (3-7)
Like compulsive buyer heading out in rage? (7,3)
I haven't cracked this one yet — but Times for the Times have:
a compulsive buyer could be SHOPPING MAD, lose the heading S.
Notes are foolish (4)
Military alliance in combat ultimately possesses death instinct (8)
I haven't cracked this one yet — but Times for the Times have:
NATO (military alliance) inside T, HAS (end of combaT, possesses). The Greek word for death, and the God who personified death. Freud wrote about the concept of thanatos and eros being the instincts for death and life, bringing the word into present day usage.
Reverse vehicle into space initially unavailable: good advice? (6)
I haven't cracked this one yet — but Times for the Times have:
CAR is reversed into (H)OLE = space, initial letter unavailable.
Someone adored at home entertaining company (4)
Youngster turned out for walk in park (6,4)
Crawl as cops seen in room (6,4)
Hammer-thrower in village rendered powerless? (4)
I haven't cracked this one yet — but Times for the Times have:
THORP (old word for a village or hamlet) loses its P for power.
Down
Soup's borscht, hot, stirred with bit of cream (6,5)
Dried out? Bowled in almost drunk before party! (7,2)
I haven't cracked this one yet — but Times for the Times have:
B for bowled, inside SO(T) = almost drunk, ERE = before, DUP = party (as in Northern Ireland politics).
Man unknown across the pond can take ecstasy (4,3)
Sound manoeuvre at sea, if in storm, when crossing succeeded (6,2,7)
Sloth and one near it disturbed (7)
Prophet or a swami putting foot over head? (5)
I haven't cracked this one yet — but Times for the Times have:
A GURU = a swami, has his U moved to the top.
Move gradually left, drawing support (5)
At Boxing Day party: earlier sick on a sherry (11)
I haven't cracked this one yet — but Times for the Times have:
MON (day) ‘boxed’ by AT = AMONT; ILL A = sick on A, DO = party.
Special welcome Yorkshire town cherished (3,6)
Freedom to squeeze many spots? (7)
I haven't cracked this one yet — but Times for the Times have:
This was my LOI as I couldn’t see the logic for a while. I think it is NO TIES (freedom) with C (a hundred, = many) squeezed in. Nothing to do with liberty to attack your acne.
Access exit with desperate determination? (2-2-3)
Catches on thin branches (5)
Back hawk-headed god seen in Athenian market (5)
Type letters or click words in the clue