Admirer cheers following popular princess (7)
I believe the answer is:
infanta
'princess' is the definition.
(I've seen this before)
'admirer cheers following popular' is the wordplay.
'admirer' becomes 'fan' (fan is a kind of admirer).
'cheers' becomes 'ta' (both can informally mean thank you).
'following' is a charade indicator (letters next to each other).
'popular' becomes 'in'.
'fan'+'ta'='fanta'
'fanta' after 'in' is 'INFANTA'.
(Other definitions for infanta that I've seen before include "member of the Spanish royal family" , "Spanish princess" , "foreign title" , "Spanish monarch's daughter" , "European royal" .)