Desire fellow animal doctor? (5)
I believe the answer is:
'desire' is the definition.
(I know that covet is a more specific form of the action begrudge)
'fellow animal doctor?' is the wordplay.
'fellow' becomes 'co' (eg a co-worker is a fellow worker).
'animal doctor?' becomes 'vet' (veterinarian).
(Other definitions for covet that I've seen before include "Jealously desire" , "Wish for something" , "Yearn to possess (an item owned by another)" , "Desire (often someone else's property)" , "Long to have (something belonging to another)" .)