Former lover putting on a French green top (6)
I believe the answer is:
vertex
'top' is the definition.
(vertex can mean something's highest point)
'former lover putting on a french green' is the wordplay.
'former lover' becomes 'ex' (an ex-lover).
'putting on' means one lot of letters go next to another.
'a french green' becomes 'vert' ('green' in French).
'ex' put after 'vert' is 'VERTEX'.
(Other definitions for vertex that I've seen before include "where sides meet" , "Corner (of triangle)" , "Summit" , "Top, apex" , "Crown, apex" .)