Person one is no longer burning for (3,5)
I believe the answer is:
old flame
'person one' is the definition.
The definition suggests a singular noun which matches the answer.
'no longer burning for' is the wordplay.
'no longer' becomes 'old' (both can mean former).
'burning for' becomes 'flame' (I am not sure about this - if you are sure you should believe this answer much more).
'old'+'flame'='OLD FLAME'
'is' acts as a link.
Can you help me to learn more?
(Other definitions for old flame that I've seen before include "Someone once loved" , "Former sweetheart" , "Ex-lover - the fire still burns" , "Ex" , "Former lover" .)