Resign from raising pets, not happy (4,4)
I believe the answer is:
step down
'resign' is the definition.
(I've seen this before)
'raising pets not happy' is the wordplay.
'raising' says the letters should be written backwards.
'not happy' becomes 'down' (down can mean sad).
'pets' back-to-front is 'step'.
'step'+'down'='STEP-DOWN'
'from' acts as a link.
(Other definitions for step down that I've seen before include "Resign, retire" , "Withdraw from" , "Gradually reduce - resign" , "Leave office" , "Give up or retire from a position" .)