First Lady having concern ultimately quits (4)
I believe the answer is:
even
'quits' is the definition.
(as in 'call it quits')
'first lady having concern ultimately' is the wordplay.
'first lady' becomes 'eve' (first woman in the Bible).
'having' means one lot of letters go next to another.
'ultimately' indicates one should take the final letters.
The last letter of 'concern' is 'n'.
'eve'+'n'='EVEN'
(Other definitions for even that I've seen before include "50-50" , "Deep crisp snow seen on Boxing Day also this" , "Commensurate" , "Equable" , "Yet; smooth" .)