The answer to your question lies in what follows "clerk@"
If it is an email service provider contracted and paid for by the council then the council owns the IP for all of the content within that mailbox and there should only be a minimal / reasonable amount (none really but a little bit is often considered reasonable) 'personal' content. And when I say personal content I mean personal to that former employee as a private individual - maybe a correspondence with a utilities provider for example. That which is 'sensitive' information (personal details of other parties conducting business with the council via the clerk) is non exclusive and sensitive for the former employee - it is sensitive for the organisation / data controller so falls under corporate protection and sensitivities. Further, if it is a council provided email service there 'should be' IT / communications policy which 'should' state that all / any email correspondence is subject to scrutiny / monitoring by appropriate person. In this case, you contact the email service provider to tell them the former employee has departed, you ask for password reset and the council nominates some person(s) to monitor the clerk email address until the situation is resolved.
If however, it is "clerk@" hotmail / iCloud / Gmail etc, then that account may well have been set up by the former employee and only they can liaise with the email service provider and your council is in a bit of a spot....
Councils really should be on .gov email accounts with a IT policy which allows and overtly states that email is monitored.