Across
Sends out one's appeals (6)
Strong defence of royal assistant from reporter (8)
I haven't cracked this one yet — but Times for the Times have:
A reporter might be (mis)heard to say PALACE AIDE for royal assistant.
Appliance for cooking tough rabbit heads (6,4)
Stone arguably regularly deficient (4)
I haven't cracked this one yet — but Times for the Times have:
The odd letters of aRgUaBlY go missing.
Voluntary work, a lot in labouring (8)
I haven't cracked this one yet — but Times for the Times have:
Work is OP and then add an anagram (labouring) of A LOT IN.
One of us English showing compassion (6)
I haven't cracked this one yet — but Times for the Times have:
I assume most of us are HUMAN (AI’s not yet good enough!). Add E[nglish].
Prime minister of northern country forgetting first two points (4)
I haven't cracked this one yet — but Times for the Times have:
Anthony of that family, luckless successor to Churchill whose downfall was precipitated by the Suez crisis of 1956. Remove the first two letters of SWEDEN, which happen also to be compass points.
Fabulous creature's alien character grasped by child (8)
City companion wearing a short outfit (3,5)
I haven't cracked this one yet — but Times for the Times have:
Companion is the (US) BUD. Clothe him with A HABIT for outfit shortened by removing the T.
Easily cowed, I'm alarmed by motorway (4)
I haven't cracked this one yet — but Times for the Times have:
Might be easily cowed but not a bad price to pay for inheriting the Earth. If I’m alarmed, I might utter EEK(!) here by M[otorway]. “By” allows you to place the letter before or after.
Dog that is mainly East European (6)
I depend on girl related to astronomer (8)
I haven't cracked this one yet — but Times for the Times have:
I LEAN for I depend (on) attached to GAL for girl.
Good feeling for music equipment (4)
I haven't cracked this one yet — but Times for the Times have:
G[ood] EAR translating feeling for music.
Prepare old crime boss for catastrophic conflict (10)
An urgent call about top-quality fireproofing (8)
I haven't cracked this one yet — but Times for the Times have:
An urgent call is A S.O.S. Insert BEST for top quality.
Restricting crossing river is causing strain (6)
I haven't cracked this one yet — but Times for the Times have:
TYING for restricting with R[iver] inserted.
Down
Small instrument out of tune (5)
Not affected by exhausted urchin feeding in frenzy (9)
Austere European novelist (6)
In sporting contest a cramp simply worsens with age (10,5)
I haven't cracked this one yet — but Times for the Times have:
An anagram (worsens) of A CRAMP SIMPLY and AGE
Be keen to pass on writing with pen (8)
Jostling crowd's right to enter film (5)
I haven't cracked this one yet — but Times for the Times have:
R[ight] takes its place in SCUM for film.
Girl presented risk, squandering initial security (9)
I haven't cracked this one yet — but Times for the Times have:
Chambers “a security issued by a company for money borrowed on the company’s property”. A girl presented is a DEB[utant]. Contributors from higher levels of society than me can let us know if it still happens. Add VENTURE for risk with its first letter deleted.
Name ships in book (9)
Realised line may achieve the same as doing this? (6-3)
I haven't cracked this one yet — but Times for the Times have:
Realised gives TUMBLED, and line R[ailwa]Y. A washing line and a tumble drier, under the right circumstances, have the same effect. The grammar’s a bit iffy and the definition underlining is flexible.
Lion, say, caught in a desert, falls (8)
I haven't cracked this one yet — but Times for the Times have:
noun. A lion is a CAT, add C[aught] inserted into A plus RAT for desert.
Promise extreme hardship (6)
I haven't cracked this one yet — but Times for the Times have:
A double definition. Aficionados of the Anglican wedding service know about “thereto I plight thee my troth”.
Dresser generally holds material (5)
Coffee substitute that comes in a cup (5)
I haven't cracked this one yet — but Times for the Times have:
Particularly during WWII, acorns were used in Germany for ersatz coffee, since the beans weren’t readily available. Acorns in their natural state come in quaint little cups.
Type letters or click words in the clue