Follow graduate in teaching (5)
I believe the answer is:
dogma
'teaching' is the definition.
(dogma is a kind of teaching)
'follow graduate' is the wordplay.
'follow' becomes 'dog' (I've seen this before).
'graduate' becomes 'ma' (abbreviation for Master of Arts).
'dog'+'ma'='DOGMA'
'in' acts as a link.
(Other definitions for dogma that I've seen before include "Body of creed" , "Tenet" , "Set of principles laid down as incontrovertibly true" , "Set of beliefs" , "Blind faith required" .)