Old queen with no love for a new one (4)
I believe the answer is:
anne
'old queen' is the definition.
(Queen Anne)
'no love for a new one' is the wordplay.
'no' indicates named letters should be taken away.
'love for' becomes 'o' (I've seen this in other clues).
'a new' becomes 'an' (I've seen this in other clues).
'an'+'one'='anone'
'anone' with 'o' taken out is 'ANNE'.
'with' is the link.
(Other definitions for anne that I've seen before include "- - Hathaway, wife of Shakespeare" , "- - of Cleves" , "Stuart queen" , "She married Shakespeare" , "The Bard wooed and won her" .)