Common classes supported by lecturer (7)
I believe the answer is:
general
'common' is the definition.
(thesaurus)
'classes supported by lecturer' is the wordplay.
'classes' becomes 'genera' (I've seen this before).
'supported by' is a charade indicator (letters next to each other) (letters go below - in down clue).
'lecturer' becomes 'l'.
'genera'+'l'='GENERAL'
(Other definitions for general that I've seen before include "Common - army officer" , "position" , "Usual; overall" , "Enlarge for senior army officer" , "Catholic" .)