It is possible to get on the Nunnery lakes.
There are a number of lakes there with the main carp lakes being Bob Clarkes, D lake and A lake.
However A lake is a syndicate within the syndicate and you won't stand a chance of getting on there for several years, if ever.
You get a chance of a D lake ticket once you have been fishing on Bob's and the other lakes for a while.
Ask around when you are in Thetford and you will soon get a contact name and number.
Although I am very curious why anyone would actually want to move to Thetford!
The same people do run this syndicate and West Stow. Both syndicates have carp to over 40lb.