Debts don't die because the debtor dies.
Clearly, it is important to handle the situation carefully and sensitively but you are entitled to pursue the debtor’s estate for the sum he owed you.
You should not delay too long letting the estate know that the sum is owed. The risk for you is if the estate is dealt with and closed, and it is only discovered afterwards that the sum was owed to you, it might be too late to take steps to recover it at that point. Estates can take many months, sometimes years, to process but you shouldn’t take the risk in letting the debt go unnoticed.
There are rules set out in the Administration of Estates Act 1925, which confirm in what order funds in the estate should be paid out. If the executors get the order wrong, you can seek compensation from them. It is unusual for mistakes to be made, especially when solicitors are involved, but sometimes they happen.
The personal representatives step into the shoes of the deceased, so if court proceedings prove necessary you will sue the personal representatives. Many personal representatives will try to reach a commercial settlement rather than litigate in the courts if there is a dispute over the sum claimed, as litigation will only likely deplete the money available in the estate. So before issuing proceedings, you should send a letter seeking payment and give them a reasonable time to respond.
Dealing with probate can be a slow process so you should not expect a quick a response. However, the personal representatives or solicitor dealing should be able give you an idea of when they can confirm whether the sum claimed is agreed or not and if agreed, when they will be able to make payment.