Elder has finished with yearning (7)
I believe the answer is:
doyenne
'elder' is the definition.
(thesaurus)
'finished with yearning' is the wordplay.
'finished' becomes 'done' (both can mean completed).
'with' indicates putting letters inside.
'yearning' becomes 'yen' (yen is a kind of yearning).
'done' going around 'yen' is 'DOYENNE'.
'has' is the link.
(Other definitions for doyenne that I've seen before include "Female most respected in a particular field" , "Woman who is senior member of her profession" , "Respected lady" , "Senior person" , "Yon Eden (anag.)" .)