Girl gets old, having concealed name (5)
I believe the answer is:
agnes
'girl' is the definition.
(I know that Agnes is a female given name)
'gets old having concealed name' is the wordplay.
'gets old' becomes 'ages' ('age' can be a synonym of 'get old').
'having concealed' indicates putting letters inside.
'name' becomes 'n' (common abbreviation e.g. on forms).
'ages' going around 'n' is 'AGNES'.
(Other definitions for agnes that I've seen before include "Woman" , "Miss Grey" , "St --' Eve, poem by Lord Tennyson" , "Lady" , "The Eve of St. - (Keats)" .)