Garvin finally accepted in routine, the smallest of the brood (4)
I believe the answer is:
runt
'smallest of the brood' is the definition.
(the runt of the litter)
'garvin finally accepted in routine' is the wordplay.
'finally' suggests the final letters.
'accepted in' means one lot of letters goes inside another (I've seen this in other clues).
'routine' becomes 'rut' (being stuck in a rut is being stuck in a routine).
The final letter of 'garvin' is 'n'.
'n' inserted into 'rut' is 'RUNT'.
'the' is the link.
(Other definitions for runt that I've seen before include "Turn into smallest of the litter" , "Smallest animal in a litter" , "Smallest pig in litter" , "Undersized pig" , "Weakest animal in a litter" .)