At home, admirer cheers Spanish princess (7)
I believe the answer is:
infanta
'spanish princess' is the definition.
(I've seen this before)
'at home admirer cheers' is the wordplay.
'at home' becomes 'in' ('in' can be similar in meaning to 'at home').
'admirer' becomes 'fan' (fan is a kind of admirer).
'cheers' becomes 'ta' (I've seen this in other clues).
'in'+'fan'+'ta'='INFANTA'
(Other definitions for infanta that I've seen before include "noble abroad" , "Spanish monarch's daughter" , "Formerly, the daughter of a Spanish king" , "European royal" , "foreign title" .)