Depends which happened first.
Clerk, elected as councillor (resigns as clerk as they cannot be an employee whilst also being their employer), becomes chair, all ok.
Councillor, resigns, is employed as clerk (following an advertised recruitment process), perfectly ok. What must not happen, is to offered a job on the basis of their resignation. E.g. "we'll give you this job if you step down" would be illegal.
However, importantly, I. This circumstance they cannot be paid for the first 12 months, so they will be doing it for free. (That's the law).