I’m giving the example of Sweden whose carbon tax is highly regarded and which is the highest in Europe. Source
Sweden has a carbon tax of €110 / t. Source
Moreover some 45% of primary energy consumed in Sweden is nuclear and hydro making Sweden’s energy supply relatively less dependent on carbon emissions. Source
As a consequence of the carbon tax and the high share of non-fossil energy generation Sweden’s per capita carbon emissions are low by international standards (5.5 t CO2e / capita / year). Source
However, when measured by consumption Sweden’s per capita emissions are relatively high (15.4 t CO2e / capita / year). 58% of carbon consumed in Sweden is imported. Source
This makes me think that there could be tendency for expensive domestic carbon emissions, especially those not covered by the cheaper EU ETS, to be substituted with carbon embedded in imports – unless the carbon tax would apply to imports as well.