It is not an application you are submitting to the Clerk, but your nomination papers, with the names of two councillors supporting you.
The Clerk must not interfere with the process, except to ensure no Councillor nominates twice etc and that the election proceeds correctly.
So when the Chair states: the first item on the agenda is election of Chair, the Clerk passes them a piece of paper stating "there are X number of valid nomination received, they are A, B, C.
The vote can be by show of hands or by ballot paper" (if permitted by standing orders)
If someone suddenly wants a ballot paper the Clerk, who is prepared distributed ballot papers to Councillors, and because they knew who was nominated, has the correct names.
It also helps the Clerk to ensure that there will be a Chairman, by alerting the Chair that no nominations have come forward so that the Chair (and not the Clerk) can chivvy up another Councillor to step forward.
Very few Clerks are power hungry (sidenote: JW did not have the authority) they just want the job done correctly.