Jersey veterinary's first pet (1,4)
I believe the answer is:
v neck
'jersey' is the definition.
(jersey with a V-neck)
'veterinary's first pet' is the wordplay.
'veterinary's first' becomes 'v' (1st letter of 'veterinary').
'pet' becomes 'neck' (necking is a kind of petting).
'v'+'neck'='V-NECK'
(Other definitions for v neck that I've seen before include "alternative to polo?" , "Type of sweater" , "design of pullover?" , "Sort of sweater" , "Type of jumper" .)