From 'The Manual':
Renewals
Railcards can be renewed up to one month before the old Railcard expires. However there must be no break of continuity between old and new Railcards. Customers must complete and sign a new application form from the current Network Railcard leaflet and pay the appropriate Railcard price.
Always ensure the clerk fills out, stamps, and returns to you, the receipt box of the Railcard leaflet. Keep this safe should a replacement Railcard be needed due to loss/theft.