They shouldn't just stop drilling. It is a moneymaker for the country and gives the government lots of money to spend on policies which reduce the country's emissions. Norway produces lots of oil relative to the country's size so if they took it off the market, it would just come from somewhere with less standards and less commitment to the environment. They should make calculated moves which don't risk the country's economic future. Taking the biggest sovereign wealth fund in the world's money out of FF stocks is a good way to start, and doesn't jeopardize much, if anything.
Green's only purpose should be to change the dialogue, not to be given any legislative power whatsoever. They will make drastic moves which will yield economic consequences felt by the public. Reality is, people have to be in good economic circumstances to care about altruistic goals like curtailing climate change. Take those good economic circumstances away from them - and suddenly the environment is no longer much of a priority.