Pet dragon is strange baptism participant! (9)
I believe the answer is:
godparent
'baptism participant' is the definition.
(a godparent may be part of a baptism)
'pet dragon is strange' is the wordplay.
'is strange' indicates an anagram.
'pet'+'dragon'='petdragon'
'petdragon' with letters rearranged gives 'GODPARENT'.
(Other definitions for godparent that I've seen before include "Pet dragon (anag)" , "Baptism sponsor" , "as one responsible for charge" , "Religious guardian" .)