My personal view would be that if the council feels it would be helpful, then the departing clerk could be involved in the interviewing, but should not be involved in the final decision.
The departing clerk understands the job, not just as a clerk in general, but also as clerk to your particular council. If they still have the trust of the council, then their contribution could be helpful in advising the councillors delegated to make the appointment.
But since the departing clerk will not be around to take responsibility for the sucess or otherwise of the decision, it would seem best that they give advice, but not take part in the actual decision.