As a landlord, you are liable for Council Tax, when:
The property is empty and not under an assured shorthold tenancy
You rent out the property to several people, and they each have an individual tenancy agreement to occupy only part of the building - called a 'house in multiple occupation' (HMO)
The property is home to a religious community or minister of religion
The property is a residential care homes, nursing homes or hostel providing care and support.
The tenant is not liable for Council Tax, if they are on a statutory periodic tenancy (or any tenancy of a term of less than 6 months) and are non-resident. The liability will usually fall on the owner.
Empty Property Discount and Exemptions
Furnished Let - Furnished lets attract a full charge if they are unoccupied.
Unfurnished Let - This discount is discretionary to each local Authority, see discounts that may be available.