Lightly touch on that woman's achievement first (7)
I believe the answer is:
feather
'lightly touch on' is the definition.
(to feather is to touch on or move over lightly)
'woman's achievement first' is the wordplay.
'woman' becomes 'her' (her refers to a woman).
'achievement' becomes 'feat' (feat is a kind of achievement).
'first' means one lot of letters go next to another.
'her' put after 'feat' is 'FEATHER'.
'that' is the link.
(Other definitions for feather that I've seen before include "dance step" , "Part of covering of bird" , "'Birds of a . . . . . . . flock together'" , "Quill" , "English plume (de ma tante?)" .)