My preference would be to start fresh, re-rent the place in it's entirety and have full control over the tenants that will be living in my property.
I think this is essential.
As to the licensee, I am not clear what this means here.
In general my understanding of a "licensee" is a person the owner allows live in a property, who is not a tenant. Typical examples would be a lodger, who lives in a property, perhaps with the owner but does not have a tenancy.
It seems from your post that this person was brought into the property by the tenant as the tenants "licensee". There is nothing unusual about this, a tenant can have a guest, or if it is not forbidden by the lease, a lodger, or a relative, to live with them in the property they have a tenancy on.
When the tenancy ends the tenants license ends as well.
I don't see any reason why you cannot just say, that when the tenancy ends you need the property returned to you vacant. The tenants must remove all their belongings, old socks and hangers-on.
Please note that I am not a solicitor and you may need lego advice, but I hope I have given you a different way of thinking about the situation.