Part of pig or horse (7)
I believe the answer is:
trotter
This clue is a double definition.
'part of pig' is the first definition.
('trotter' is part of 'pig')
'horse' is the second definition.
(trotter is a kind of horse)
'or' acts as a link.
(Other definitions for trotter that I've seen before include "Pig's foot, or one on the run" , "foot of animal for food" , "horse getting sulky, say" , "Food for man" , "Steady horse; pig's foot" .)