One has some responsibility for this divine little creature? (8)
I believe the answer is:
godchild
'one has some responsibility for this divine little creature?' is the definition.
The answer and definition can be both people as well as being singular nouns.
Maybe you can see a link between them that I can't see?
'divine little creature?' is the wordplay.
'divine' becomes 'god' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'little creature?' becomes 'child'.
'god'+'child'='GODCHILD'
(Other definitions for godchild that I've seen before include "one who's received sponsorship" , "Sponsored youngster" , "One sponsored at christening" , "Sponsored individual" , "Sponsored baptised baby" .)