Princess rejecting old flame in addition (6)
I believe the answer is:
annexe
'addition' is the definition.
(annexe is a kind of addition)
'princess rejecting old flame' is the wordplay.
'princess' becomes 'anne' (I've seen this before).
'rejecting' is a reversal indicator (I've seen 'rejected' mean this).
'old flame' becomes 'ex' (I've seen this in other clues).
'ex' reversed gives 'xe'.
'anne'+'xe'='ANNEXE'
'in' acts as a link.
(Other definitions for annexe that I've seen before include "Addendum" , "Joined-on building" , "Additional room etc for house" , "bit on the side?" , "Side building" .)