The only way to stop people drilling for oil in new places is to kill the demand for it more quickly.
If you stop the sales of oil based new vehicles in Europe, Japan, and the US, and stop using fossil fuels to generate power in those regions, then you force most of the biggest carmakers to quickly transition to electric vehicles. Then offer people big incentives to trade in old vehicles or have them converted, and transition public transport and industry, and you very quickly would kill the demand in those areas, and the rest of the world will quickly follow.
When nobody is buying oil, then companies will stop drilling for it.