The advice from your clerk is incorrect. Not only can you elect a new Chair mid-term, you must do so as the first item of business at the next council meeting.
Under Schedule 12, Part II, paragraph 7(1) of the Local Government Act 1972, if the position of Chair is vacant, the very first order of business at the next meeting must be to elect a replacement. The council cannot conduct any other business until this has been done.
This means that any decisions made while the Chair position remains vacant would be procedurally unlawful. Until a new Chair is elected, the Vice-Chair can step in for the purposes of chairing the meeting, but they do not automatically become Chair and must not preside over decision-making beyond facilitating the election of a new chair.
There is no requirement to wait until the annual meeting (no such thing as an 'AGM') - the law is clear that the council must act at the next full meeting. An extraordinary meeting may be called specifically for this purpose if desired. If the Clerk maintains their position, I would suggest they refer to the legislation for clarification.