The Local Government Act 1972, s116 specifically states that a councillor cannot become a paid Clerk for 12 months but they can do it for free:
116 Members of local authorities not to be appointed as officers.
A person shall, so long as he is, and for twelve months after he ceases to be, a member of a local authority, be disqualified for being appointed [or elected] by that authority to any paid office, other than to the office of chairman or vice-chairman [or, in the case of a local authority which are operating executive arrangements which involve a leader and cabinet executive, the office of executive leader or member of the executive]. . ..