Across
One leaving tutors takes girl round a former African province (9)
I haven't cracked this one yet — but Times for the Times have:
TRA{i}NS (tutors) [one leaving], then VAL (girl – random female #1) containing [round] A
Of good taste, and reputed to have soft heart (5)
I haven't cracked this one yet — but Times for the Times have:
SAID (reputed) with P contained [to have (soft) heart]
Coach further, and keep, outside right (7)
Character transfixed by horse's carrying capacity (7)
Shawl originally for independent care home's use (5)
Napier's function, to record a beat, do we hear? (9)
Dollar cakes with room for moving around (9)
Gelatinous substance from a river crossing Georgia (4)
I haven't cracked this one yet — but Times for the Times have:
A + R (river) containing [crossing] GA (Georgia). Extracted from SE Asian seaweeds and used in cooking soups etc.
Sound demeanour for one who'll succeed (4)
A second-rate dyer, one avoiding the hard stuff (9)
I haven't cracked this one yet — but Times for the Times have:
A, B (second-rate), STAINER (dyer)
Row about this writer's old American car (9)
I haven't cracked this one yet — but Times for the Times have:
LINE (row) containing [about] I’M (this writer’s) + O (old) + US (American)
Stress shown by Conservative wearing new suit (5)
Largely superfluous note about Motown (7)
End of shocking scam over Greek character's dumplings (7)
I haven't cracked this one yet — but Times for the Times have:
{shockin}G [end], then CON (scam) reversed [over], CHI (Greek character). Small dumplings made with flour, semolina, or potato.
Ultimately unfriendly deed, pinching hotel vessel (5)
I haven't cracked this one yet — but Times for the Times have:
{unfriendl}Y [ultimately], ACT (deed) containing [pinching] H (hotel)
My man, the French tragic dramatist (9)
Down
A repeated phrase in Eliot initially identifying taxes (7)
I haven't cracked this one yet — but Times for the Times have:
A + RIFF (repeated phrase) contained by [in] T S (Eliot initially)
Small island rowing crew talked of (3)
In the main, it's a source of upheaval (8)
Female flautist's second record (5)
I haven't cracked this one yet — but Times for the Times have:
ANNA (female – random female #2), {f}L{autist’s} [second]
Drawn to suits, soldier in written works promises to pay (9)
I haven't cracked this one yet — but Times for the Times have:
GI (soldier) contained by [in] LIT (written works) + IOUS (promises to pay)
Home Counties woman, one married in Barcelona, say? (6)
Fantasist of dismal aspect touring Maine (7)
Alluring companion exciting Mairi's cat (11)
Practical about boxer given something to chase endlessly (9)
Beginning of work involving Italian singer (8)
Break cover, initially appearing in sloop-rigged vessel (7)
I haven't cracked this one yet — but Times for the Times have:
LID (cover) + A{ppearing}[initially] contained by [in] HOY (sloop-rigged vessel)
Pause telepathic communication during ceremony (7)
Safety device choosy users primarily promote (3-3)
Mercian king hiding in walled garden (5)
Pass school regularly (3)
I haven't cracked this one yet — but Times for the Times have:
{s}C{h}O{o}L [regularly]
Type letters or click words in the clue