Equipment to look after tailless pet (6)
I believe the answer is:
kitten
'pet' is the definition.
(cats are often kept as pets)
'equipment to look after tailless' is the wordplay.
'equipment' becomes 'kit' (kit is a kind of equipment).
'to look after' becomes 'tend' (tending is a kind of looking after).
'tailless' means to remove the last letter (the tail of the word is removed).
'tend' with its last letter taken off is 'ten'.
'kit'+'ten'='KITTEN'
(Other definitions for kitten that I've seen before include "Young rabbit" , "Little Tom, perhaps" , "Little feline" , "Baby cat" , "Mini-mog?" .)