Doting fan has circuit to follow (6)
I believe the answer is:
lapdog
'doting fan' is the definition.
(lapdog can mean a servile person)
'circuit to follow' is the wordplay.
'circuit' becomes 'lap' (synonyms).
'to follow' becomes 'dog' (dog can mean to follow or torment).
'lap'+'dog'='LAPDOG'
'has' acts as a link.
(Other definitions for lapdog that I've seen before include "One readily submitting" , "Pom, for one" , "one of man's more diminutive best friends" , "Submissive type" , "Small pampered pet" .)