The aim's to be converted, having no church (7)
I believe the answer is:
atheism
'having no church' is the definition.
(not belonging to a church or religion)
'the aim's to be converted' is the wordplay.
'to be converted' indicates an anagram.
'the'+'aims'='theaims'
'theaims' is an anagram of 'ATHEISM'.
(Other definitions for atheism that I've seen before include "Disbelief in gods" , "Non-belief in God" , "Owed" , "displaying opposition to religion" , "Disbelief in a god" .)