Gas Safe Register appear to be advising on their helpline that a landlord is obliged to obtain a new gas safety certificate every time a tenancy is entered into, notwithstanding any current gas safety certificate that is in place. This is not the position.
The Landlord (or the Agent if it forms part of the terms of business) is required to arrange the annual preparation of a gas safety certificate and ensure that throughout any tenancy a valid gas safety certificate is in place at all times.
An annual gas safety check must be carried out by a Gas Safe Registered engineer. A record of the safety check must be kept for 2 years. A copy of the certificate must be issued to each existing tenant within 28 days of the check being completed, and in any event before the commencement of a tenancy.
This is consistent with the advice as given on the Gas Safe Register website.
The relevant legislation can be read here.