There is no heir apparent in Oman and the Sultan was unmarried.BBC:
According to the the rules of the sultanate’s succession, the Royal Family Council must now choose a new sultan.
If the council of 50 male members fail to agree on a successor, then the envelope left by Sultan Qaboos will be opened.
Whoever the late Sultan named as his successor will then be enthroned
The sultan deposed his father in a bloodless coup with British support in 1970.
At the age of 29 he overthrew his father, Said bin Taimur, a reclusive and ultra-conservative ruler who banned a range of things, including listening to the radio or wearing sunglasses, and decided who could get married, be educated or leave the country.