It appears in a woman's secret birthright (8)
I believe the answer is:
heritage
'birthright' is the definition.
(synonyms)
'it appears in a woman's secret' is the wordplay.
'appears in' indicates putting letters inside.
'a woman's' becomes 'her' (belonging to a woman).
'secret' becomes 'age' (I can't explain this - if you can you should give a lot more credence to this answer).
'her'+'age'='herage'
'it' going within 'herage' is 'HERITAGE'.
Can you help me to learn more?
(Other definitions for heritage that I've seen before include "Their age (anag.)" , "Patrimony" , "historical collection?" , "Property or practices passed down" , "Valued survivals from the past" .)