Soft piece of velvet, nice to stroke (3)
I believe the answer is:
pet
'to stroke' is the definition.
(I know that caress is the is a more specific form of the action of pet.)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for pet that I've seen before include "Bad humour; darling" , "Tamed animal; sulk" , "Favourite, perhaps a domestic animal" , "Tamed domestic animal" , "Favourite pupil" .)