Admirer cheers to support popular princess (7)
I believe the answer is:
infanta
'princess' is the definition.
(I've seen this before)
'admirer cheers to support popular' is the wordplay.
'admirer' becomes 'fan' (fan is a kind of admirer).
'cheers' becomes 'ta' (both can informally mean thank you).
'to support' says to put letters next to each other (in a down clue, some letters hold others up).
'popular' becomes 'in' ('in' can mean trendy).
'fan'+'ta'='fanta'
'fanta' after 'in' is 'INFANTA'.
(Other definitions for infanta that I've seen before include "Royal personage" , "noble abroad" , "member of the Spanish royal family" , "King of Spain's daughter" , "King's daughter" .)