Tears flowing about man and woman (7)
I believe the answer is:
theresa
'woman' is the definition.
'tears flowing about man' is the wordplay.
'flowing' is an anagram indicator.
'about' means one lot of letters goes inside another.
'man' becomes 'he' (pronoun for a man).
'tears' anagrammed gives 'tresa'.
'tresa' going around 'he' is 'THERESA'.
'and' acts as a link.
(Other definitions for theresa that I've seen before include "May's one" , "Maria ___ , Archduchess of Austria, d. 1780" , "Lisieux saint" , "-- May, MP" , "Girl's name" .)