The woman and man run after (3)
I believe the answer is:
her
'the woman' is the definition.
('her' refers to a woman)
'man run after' is the wordplay.
'man' becomes 'he' (he refers to a man).
'run' becomes 'r' (cricket abbreviation).
'after' says to put letters next to each other.
'he'+'r'='HER'
'and' acts as a link.
(Other definitions for her that I've seen before include "That lady" , "That lady's" , "Belonging to a female" , "The female's" , "She, objectively" .)