Across
Animal's awfully cute rear (8)
To obtain acknowledgement, order direct (6)
I haven't cracked this one yet — but Fifteensquared have:
anagram/”order” of (direct)* “To obtain” in the surface is part of the instructions (to get to a definition of “acknowledgement”, do this…)
Have a break! Have a ginger biscuit! (4)
Having many factories on River Test (10)
Aerial transport suggested for the prairies (6)
Book on trendy South Coast resort (8)
Reprimands favourite fellow travellers? (7)
Hatbands for mourners (7)
Rugby international follows a VIP eccentric to clubhouse (8)
I haven't cracked this one yet — but Fifteensquared have:
LION=”Rugby international”, after anagram/”eccentric” of (a VIP)* the British and Irish Lions are a rugby union team [wiki]
Foreigner needs help back into lodging (6)
I haven't cracked this one yet — but Fifteensquared have:
AID=”help” reversed/”back” inside INN=”lodging”
Spin doctor live, on tour (10)
Exhausted marksman (4)
Stop dead and liberate heartless zombie (6)
Contents from small Red strongholds (8)
Down
Lawn weed? Cut the whole lot up (8)
Bulb – its brightness? (4)
I haven't cracked this one yet — but Fifteensquared have:
not sure about this – LAMP can refer to a light bulb, and is associated with brightness, but I can’t see more than that edit: Simon S in the comments suggests L + AMP (50 amp) I think I have seen “50 amp” in wordplay before to give LAMP
Vengeful trio that is wearing winter outfits (6)
Originally named 'Beds' – to change is necessary (5-2)
I haven't cracked this one yet — but Fifteensquared have:
for definition, e.g. ‘if needs-be’ / ‘if necessary’ NEE (née, “Originally named”), plus anagram/”to change” of (Beds)*
Middle East and Sicily somehow give rise to unfriendly grin (3,5)
I haven't cracked this one yet — but Fifteensquared have:
anagram/(the letters “somehow give rise to…”) of (ME Sicily)*, with ME short for Middle East
Horribly wrong, like certain Satie compositions (4-6)
I haven't cracked this one yet — but Fifteensquared have:
I had to look this up: the composer Satie wrote Three Pieces in the Shape of a Pear [wiki]
One of the Kardashians upset over a party for emperor (6)
I haven't cracked this one yet — but Fifteensquared have:
definition: a term referring to the emperor of Japan KIM=”One of the Kardashians” [wiki] reversed/”upset”; plus A (from surface) + DO=”party”
Surprising dim person I kept behind bars (10)
Magistrates taking native American families around UN (8)
Chooses to run again arranging ad and poster (2-6)
St Paul's destination, travelling to China (7)
Egyptian god from tops of ancient monument near ruins (4,2)
I haven't cracked this one yet — but Fifteensquared have:
top letters of A-ncient M-onument; plus anagram/”ruins” of (near)*
Pub 'Half of 21' for fictional purposes (2,4)
Precipitation ultimately unknown in Tamworth, perhaps? (4)
I haven't cracked this one yet — but Fifteensquared have:
last/ultimate letter from [unknow]-N, in SOW (Tamworth is a breed of pig)
Type letters or click words in the clue