Going to slightly disagree here for the purpose of clarity. If an additional meeting is required for ordinary business, it is the clerk who signs the agenda (in effect therefore, convening the meeting).
There's actually no such thing as an EGM or an AGM for that matter. An extraordinary meeting is a meeting which is requested by two or more councillors or can be convened by the Chair and the agenda is signed by the requesting councillors or the Chair as required rather than the Clerk. In practice, it is usually the clerk who actually prepares the agenda/notices/supporting documents if only to ensure all the necessary legal requirements are met) but I do appreciate that where the issue is contentious and not agreed by full council that might not happen.
Sometimes an additional meeting is required for what might be considered "ordinary" business such as to consider a planning application or an urgent matter which cannot wait until the next scheduled meeting. In this case it can be argued that it is an ordinary meeting or is sometimes referred to as an additional ordinary meeting or I've even seen it as extra ordinary meeting. It's confusing but my view is that if something needs doing, the semantics of what it's called are irrelevant.