After gym, family starts to exercise strong, eager, dog (8)
I believe the answer is:
pekinese
'dog' is the definition.
(Pekinese is an example)
'after gym family starts to exercise strong eager' is the wordplay.
'after' is a charade indicator (letters next to each other).
'gym' becomes 'pe'.
'family' becomes 'kin' ('kin' can be a synonym of 'family').
'starts to' suggests taking the first letters.
The first letters of 'exercise strong eager' is 'ese'.
'pe' put next to 'kin' is 'pekin'.
'pekin'+'ese'='PEKINESE'
(Other definitions for pekinese that I've seen before include "Small short-legged dog with a long silky coat" , "Snub-nosed dog breed" , "Small pet dog" , "(Chinese) dog" , "Small breed of dog" .)