Restrain mongrel beginning to bite (4)
I believe the answer is:
curb
'restrain' is the definition.
('curb' can be a synonym of 'restrain')
'mongrel beginning to bite' is the wordplay.
'mongrel' becomes 'cur' ('cur' can be a synonym of 'mongrel').
'beginning to' says to take the initial letters.
The first letter of 'bite' is 'b'.
'cur'+'b'='CURB'
(Other definitions for curb that I've seen before include "Check or restrain" , "Bridle" , "'Temper, hold in restraint (4)'" , "Constrain" , "[LIMITATION]" .)