Following a line (7)
I believe the answer is:
pursuit
This clue is a double definition.
'following' is the first definition.
('pursuit' can be a synonym of 'following')
'a line' is the second definition.
(thesaurus)
(Other definitions for pursuit that I've seen before include "See 1" , "Hobby" , "Interest" , "The chase or the occupation" , "recreational activity" .)