Well it can continue function whilst seeking a Clerk (through an appointed internal or external Locum (deputy acting up as Clerk) or a temporary unpaid appointment from within Cllr membership) but ultimately all Town/Parish/Community Councils need an appointed permanent proper officer to function effectively and move things forward. It's not a good place for any Council to find themselves in. You ideally want a managed handover (accept not always possible for a variety of reasons depending on nature of departure)