If there is a Will it will name the Executors. The Executors are not obliged to take up the role and can refuse to act. Where they do act their authority derives from the will and the Grant of Probate provides the validation that the Will presented is proved to be the last will of the deceased. If the Executors are unwilling or unable to act the Will remains valid and administrators would be appointed to obtain probate.
If there is no Will the deceased will have died intestate. Intestacy is a term whereby the entitlement to the estate is determined by law. Those entitled to the estate are permitted to apply for a Grant of Probate. There is an order of priority as to who has first refusal to apply. Once the Grant is obtained they have the authority to deal with the winding up of the estate as per an Executor.