Supporter of that woman through a depression (8)
I believe the answer is:
adherent
'supporter' is the definition.
(I've seen this in another clue)
'that woman through a depression' is the wordplay.
'that woman' becomes 'her' ('her' refers to a woman).
'through' is an insertion indicator (inserted letters go through the word).
'depression' becomes 'dent' (synonyms).
'a'+'dent'='adent'
'her' placed into 'adent' is 'ADHERENT'.
'of' acts as a link.
(Other definitions for adherent that I've seen before include "One supporting" , "Staunch follower" , "Supporter, fan" , "Disciple, follower" , "advocate" .)