Death of a director

The sole director and shareholder of one of my clients has unexpectedly died. The beneficiary wishes the company to continue however as its very early days, the structure of this has yet to be decided. What are the legal implications? presumably a new direcor, even if only temporary has to be appointed asap? Do the banks need to be notified asap aswell and will this freeze the company bank accounts as this will make the company very difficult to continue to run? There is some dispute as to whether the executors are accepting appointment to act as executors. Any advice very gratefully received.