Island out of Defoe, possibly originally associated with old bit of Britain (7)
I believe the answer is:
danelaw
'old bit of britain' is the definition.
(historically, part of England ruled by the Danes)
'island out of defoe possibly originally associated' is the wordplay.
'island' becomes 'i' (geographical abbreviation).
'out of' suggests deleting specific letters ('out of' can mean no longer having).
'defoe possibly' becomes 'Daniel' (as in the author Daniel Defoe).
'originally associated' becomes 'aw' (I can't justify this - if you can you should give a lot more credence to this answer).
'daniel' with 'i' taken away is 'danel'.
'danel'+'aw'='DANELAW'
'with' is the link.
Can you help me to learn more?
(Other definitions for danelaw that I've seen before include "Northern part of England when under foreign rule" , "Viking-occupied England" , "old north" , "Part of country once" , "Area of England settled by Vikings" .)