Nearly all getting into animal doctor’s clean car (5)
I believe the answer is:
valet
'clean car' is the definition.
(valet can mean to clean a car)
'nearly all getting into animal doctor's' is the wordplay.
'nearly all' becomes 'al'.
'getting into' is an insertion indicator.
'animal doctor' becomes 'vet' (veterinarian).
'al' placed into 'vet' is 'VALET'.
(Other definitions for valet that I've seen before include "Gentleman%u2019s gentleman" , "Jeeves?" , "'No man is a hero to his . . . . .'" , "Personal manservant" , "Clean (a car); attendant" .)