Girl is holding on in attempts to win converts (8)
I believe the answer is:
missions
'attempts to win converts' is the definition.
(as in religious missionaries)
'girl is holding on' is the wordplay.
'girl' becomes 'miss' (term of address for an unmarried woman).
'holding' is an insertion indicator.
'is' placed around 'on' is 'ions'.
'miss'+'ions'='MISSIONS'
'in' acts as a link.
(Other definitions for missions that I've seen before include "Bombing raids" , "religious buildings - with 14a" , "Journeys for scientific, military or religious purpose" .)