Vet dropping soft animal (6)
I believe the answer is:
insect
'animal' is the definition.
(insect is a kind of animal)
'vet dropping soft' is the wordplay.
'vet' becomes 'inspect' (inspect can mean to vet or check).
'dropping' indicates named letters should be taken away.
'soft' becomes 'p' (musical abbreviation for 'piano').
'inspect' with 'p' removed is 'INSECT'.
(Other definitions for insect that I've seen before include "Worthless person" , "Small, usually winged, creature" , "Six-legged animal" , "Creepy-crawly" , "Small invertebrate creature" .)