The Chair cannot act on their own, in any circumstance. It should be down to the Full Council or the personnel committee to decide if they want to reinstate the Clerk or not. Of course, this would have to be in private session and without the Clerk present.
If they decide that they don't want the Clerk to remain, they will have to insist they leave. If they want the Clerk to remain, they will probably have to write a formal letter to confirm this and that the period of employment has been continuous. I would suggest that as the Clerk has continued working beyond the notice period and there has been no object from the Council that the latter is wanted.