That woman takes a catch (4)
I believe the answer is:
hear
'catch' is the definition.
(to catch something is to hear it being spoken)
'that woman takes a' is the wordplay.
'that woman' becomes 'her' ('her' refers to a woman).
'takes' is an insertion indicator.
'her' going around 'a' is 'HEAR'.
(Other definitions for hear that I've seen before include "Pick up, aurally" , "Find out" , "Perceive with the ear" , "to judge" , "Discover aurally" .)