Part of process seeing return of animals at home (4)
I believe the answer is:
step
'part of process' is the definition.
(a step is part of a process)
'return of animals at home' is the wordplay.
'return of' is a reversal indicator.
'animals at home' becomes 'pets' (pets are animals kept in the home).
'pets' back-to-front is 'STEP'.
'seeing' acts as a link.
(Other definitions for step that I've seen before include "Put foot on a pest" , "Football" , "Movement in dancing" , "Place foot on as with a pest" , "Part of a stairway" .)