Mark pursues mother with a cosmetic (7)
I believe the answer is:
mascara
'cosmetic' is the definition.
(I know that mascara is a type of make-up)
'mark pursues mother with a' is the wordplay.
'mark' becomes 'scar' (mark left by an injury).
'pursues' means one lot of letters go next to another.
'mother' becomes 'ma' (Ma is another word for mother or mum).
'with' means one lot of letters go next to another.
'scar' after 'ma' is 'mascar'.
'mascar'+'a'='MASCARA'
(Other definitions for mascara that I've seen before include "black application" , "could be found in handbag, perhaps" , "Cosmetic for the eyes" , "Make-up item" , "Cosmetic for darkening the eyelashes" .)