First woman to follow exercise bug (5)
I believe the answer is:
peeve
'bug' is the definition.
(both can mean to annoy)
'first woman to follow exercise' is the wordplay.
'first woman' becomes 'Eve' (first woman in the bible).
'to follow' means one lot of letters go next to another (some letters go after or follow others).
'exercise' becomes 'pe' (Physical Education).
'eve' put after 'pe' is 'PEEVE'.
(Other definitions for peeve that I've seen before include "Cause annoyance" , "Cause resentment" , "Get annoyed" , "cause irritation" , "Annoy, get at, irritate" .)