Not really the type to live a bit chastely! (5)
I believe the answer is:
beast
'not really the type' is the definition.
I can't judge whether this defines the answer.
'live a bit chastely' is the wordplay.
'live' becomes 'be' ('be' can be a synonym of 'live').
'bit chastely' becomes 'st' (I can't explain this - if you can you should give a lot more credence to this answer).
'be'+'a'+'st'='BEAST'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for beast that I've seen before include "Animal; cruel person" , "Pig" , "Bully" , "Brute; creature" , "Animal, creature" .)