Frequently, as executor or trustee, you will first want to run an appropriate Notice to Creditors. In North Carolina, the Notice to Creditors must allow at least 3 months for creditors to respond. Frequently, bills and debts will not be paid until after this 3 month window to assure that they are paid in the appropriate order of priority. However, with a larger estate where there is clearly sufficient assets to cover any debts and expenses, some bills and expenses may be paid sooner.
As the executor or trustee, it is also your duty to ensure that the bills and debts are bona fide and legally enforceable.