Non-specific (7)
(Other definitions for general that I've seen before include "Common - soldier" , "Not specialised or limited" , "Army rank" , "Regular - officer" , "blanket" .)
'non-specific' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for generic that I've seen before include "Referring to a whole class or group" , "(Of drugs) having no brand name" , "Unspecific" , "of no specific type" , "appropriate for the whole class" .)