Across
Cooks tofu in a stew, admitting starter of turkey is unavailable (3,2,5)
I haven't cracked this one yet — but Times for the Times have:
Anagram [in a stew] of COOKS TOFU containing [admitting] T{urkey} [starter]
Slightly move the jug (4)
Open gothic novel suitable for a film? (10)
Twin reported for fight (4)
Give up TV for a toy (4-2-3-3)
5:37, perhaps, is when most are watching? (5,4)
I haven't cracked this one yet — but Times for the Times have:
The format 5:37 is used for displaying time of the day and the digits here are all prime numbers. The definition continues the TV theme from the previous clue.
Opportunely gathering trendy material for a coat? (5)
Private place to drink beer occasionally (5)
I haven't cracked this one yet — but Times for the Times have:
INN (place to drink), {b}E{e}R [occasionally]
Short street party is swell (9)
One flat, say, with important endorsement (3,9)
I live with cross mountain climber? (4)
Fairy queen avoiding difficulty to get flower (10)
I haven't cracked this one yet — but Times for the Times have:
PERI (fairy), W{r}INKLE (difficulty) [avoiding queen – R). Wiki: A peri is a fairy-like creature in Middle Eastern and Asian mythology.
Head of innovation not in running for award (4)
Spy pens farewell, initially navigating in a new direction (2,1,7)
I haven't cracked this one yet — but Times for the Times have:
AGENT (spy) contains [pens] TA-TA (farewell) + N{avigating} [initially]
Down
Henhouses with no roof? My mistake! (4)
I haven't cracked this one yet — but Times for the Times have:
{c}OOPS (henhouses) [with no roof]
Writer shuns a universal god (4)
I haven't cracked this one yet — but Times for the Times have:
{au} THOR (writer) [shuns a universal]. I had this originally as THOR{au} and suspected an error in the clue as the famous American writer is spelt ‘Thoreau’ but there’s nothing to indicate deletion of the ‘e’. Anyway it turns out that the error was my own since the wordplay is much more simple than I was trying to make it. Many thanks to Kevin Gregg for pointing this out and to Bletchley Reject for considering the same route to the answer as mine, although he was wise enough to reject it and think again. [Edited at 05:50 BST]
Cheese from farm fair goes rotten (7,5)
Pinch whiskey in wooden container (5)
Customers tell niece off (9)
Hit Scotsman over pinching bishop's instrument (5,5)
I haven't cracked this one yet — but Times for the Times have:
THUMP (hit) + IAN (Scotsman) + O (over), containing [pinching] B (bishop). Also called ‘mbira’ or ‘sansa’ this is a musical instrument of southern Africa consisting of a set of keys or tongues attached to a resonator, which are plucked with the thumb and forefingers. (SOED). I never heard of it. All searches on YouTube return music for the kalimba which seems to another name for it, or a very similar instrument
Briefly cancel boring family member's leisure (10)
Party official's business working to capture one arachnid (4,8)
I haven't cracked this one yet — but Times for the Times have:
WHIP’S (party official’s), then CORP (business) + ON (working) containing [to capture] I (one). Another unknown to me. A party whip is an MP appointed to maintain discipline and ensure that fellow members vote in accordance with party policy.
Dusting sign on top of library during cleaning period? (10)
I haven't cracked this one yet — but Times for the Times have:
INK (sign) + L{ibrary} [top] contained by [during] SPRING (cleaning period)
Cook binned a key ingredient for chilli (6,4)
Live together (2,7)
Informally, it is not corrupt? (5)
I haven't cracked this one yet — but Times for the Times have:
T’AINT (it is not) [informally]
Island beginning to erupt — heavens above! (4)
Coin dispatched to the auditors (4)
Type letters or click words in the clue