Tenant Vacating Property Early & Repayment of Deposit

Other

You must make it quite clear (and it should be stated in the contract document which they signed) that the tenants are responsible for any rent due during the period of the agreement, until such time as you find a new tenant.
I would hang on to the deposit until the contractual end of the tenancy unless you get a new tenant in sooner. Then your existing tenant has to agree to forfeit the deposit - absolute madness I agree, but that is the scenario. You cannot just take it as payment toward unpaid rent. THe TDS law is on the tenant side always!