Let's not have bird shivering: it's uncivilised (7)
I believe the answer is:
heathen
'uncivilised' is the definition.
(thesaurus)
'let's not have bird shivering' is the wordplay.
I cannot really see how this works, but
'have' could be 'eat' (eating is a kind of having) and 'eat' is found within the answer.
'bird' could be 'hen' (hen is a kind of bird) and 'hen' is located in the answer.
A single letter 'h' remains which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).
'it's' acts as a link.
(Other definitions for heathen that I've seen before include "Uncultured" , "Infidel, pagan" , "One who doesn't acknowledge your god" , "Barbaric" , "Non-believer" .)