Stopping it would be useless, it'd just increase production from oil wells of other countries. They could invest that money into accelerating green technology.
Of course second order effects might dwarf that, like the fact that increasing prices would incentivize oil extraction in currently unprofitable locations. That extraction may or may not be more carbon-intensive than Norway's (though probably more if it's currently unprofitable).
It sounds punchy to say "Norway should stop extracting oil" as much as it does to say "It doesn't matter whether they do or not since someone else will", but the reality is much more complex than either of those simplistic zeroth-order approximations.
The only real change from such a policy is how quickly wells will run dry, but I hope we can abandon oil long before running out is a serious concern.
Sure, other wells will produce more. But at a higher price. Higher prices encourage use of greener alternatives.
It bootstraps companies like Tesla, and VW's electric cars. That will lead to more CO2 reductions happening sooner.