Dog exercise class -- family pet seen regularly (8)
I believe the answer is:
pekinese
'dog' is the definition.
(Pekinese is an example)
'exercise class family pet seen regularly' is the wordplay.
'exercise class' becomes 'pe' (physical education).
'family' becomes 'kin' ('kin' can be a synonym of 'family').
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'pet'+'seen'='petseen'
The alternating letters of 'petseen' are 'ese'.
'pe'+'kin'+'ese'='PEKINESE'
(Other definitions for pekinese that I've seen before include "Snub-nosed dog breed" , "Small short-legged dog with a long silky coat" , "Small breed of dog" , "Small pet dog" , "like some Asian citizens" .)