Part of a circle (7)
(Other definitions for segment that I've seen before include "split up" , "Part, piece" , "One part of a whole" , "Part of a circle cut off by a chord" , "Gets men with part cut off" .)
'part of a circle' is the definition.
('arc' is part of 'circle')
This is the entire clue.
(Other definitions for arc that I've seen before include "development of plot" , "section of Circle Line" , "bends?" , "Part of a circle's circumference" , "A curve for Joan of . . ." .)