This writer was first to admit depression and softened (8)
I believe the answer is:
mellowed
'softened' is the definition.
(mellowing is a kind of softening)
'this writer was first to admit depression' is the wordplay.
'this writer' becomes 'me' (the person who is writing these clues).
'was first' becomes 'led'.
'to admit' means one lot of letters goes inside another.
'depression' becomes 'low' ('low' can be a synonym of 'depression').
'led' enclosing 'low' is 'llowed'.
'me'+'llowed'='MELLOWED'
'and' is the link.
(Other definitions for mellowed that I've seen before include "Grown soft and pleasant with age" , "Matured" , "Became softer" , "Softened by maturity" .)