A follower on the edge of the verge (4)
I believe the answer is:
brim
'the verge' is the definition.
(thesaurus)
'a follower on the edge' is the wordplay.
'a follower' becomes 'b' ('b' is the follower of 'a' in the alphabet).
'on' says to put letters next to each other.
'the edge' becomes 'rim' (rim is a kind of edge**).
'b'+'rim'='BRIM'
'of' acts as a link.
(Other definitions for brim that I've seen before include "Top edge of a container" , "Edge (of cup or hat)" , "Projecting edge of hat" , "Lip; part of a hat" , "Edge around a hat" .)