From the Regulation:
FCL.905.CRI CRI — Privileges and conditions
(a) The privileges of a CRI are to instruct for:
(1) the issue, revalidation or renewal of a class or type rating for single-pilot aeroplanes,
except for single-pilot high performance complex aeroplanes, when the privileges sought by
the applicant are to fly in single-pilot operations;
Renewal of a Class rating can only occur if the candidate holds a Class Rating, which means they are a qualified pilot. Any training may therefore be conducted by a CRI or FI. The status of the licence is irrelevant as all that is required to have it reissued is paperwork.