They should replace it with synthetic hydrocarbon fuels made from CO2, water and energy from non-carbon sources, including nuclear as well as renewables.
The underlying technology for synthesising hydrocarbons as been around for 100 years and is well understood. Oil companies have huge numbers of chemical engineers and are perfectly capably of deploying it at industrial scale, if they have an incentive. Banning exploration would be an incentive to start. Banning new wells would be the next step, followed, eventually, by banning extraction altogether.
It seems to me that trying to get rid of hydrocarbon fuels is a big mistake. They are a very efficient way to store and transport energy and there are not many viable alternatives for aircraft. Moreover, there are 1.5 billion cars in the world; the overwhelming majority run on petrol or diesel and they are not going to be replaced with EVs any time soon. The problem the climate faces is the result of new CO2 being added to the atmosphere, not from the use of hydrocarbon fuels per se. Fuels that are made from CO2 that is taken out of the atmosphere using renewable or nuclear energy are net neutral.
Getting the oil companies to switch from pumping oil out of the ground to making oil from CO2 and H2O has the potential to make 1.5 billion vehicles carbon neutral without the trillions on capital expense to replace them all, which means that it could happen much faster. It allows existing infrastructure to be reused and, if done right, would make the oil companies part of the solution. While there are some people who think oil companies are inherently evil and should be destroyed, not giving them a role in solving the problem means that you will have trillion-dollar companies fighting against change tooth and nail, because their very existence depends on it. If instead you give them a path to making a profit without pumping new oil from the ground you can have all those resources working in ways that will help the planet, not hinder it. Banning new exploration for oil is the first step in incentivising that transition.