Smitten peri had to love goddess (9)
I believe the answer is:
aphrodite
'love goddess' is the definition.
(I've seen this before)
'smitten peri had to' is the wordplay.
'smitten' indicates an anagram (past tense of smite ie to smash).
'peri'+'had'+'to'='perihadto'
'perihadto' anagrammed gives 'APHRODITE'.
(Other definitions for aphrodite that I've seen before include "Paris prizewinner" , "Greek goddess of beauty and love" , "got Paris's approval" , "Atrophied (anag.)" , "Greek goddess of love, like Roman Venus" .)