If you go to work abroad and you no longer have any income from gainful activity in Slovakia, you no longer pay insurance premium in Slovakia.
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Pay insurance premium when employed abroad
Will I still pay insurance premiums in Slovakia if I got a job abroad?
Where will I be insured if I work abroad?
From the first day of work abroad, you will be subject to the legislation of the country in which you will work. There, the employer will register you in the social system of the given country and there will also pay insurance premium for you. All obligations related to termination of employment in Slovakia were previously fulfilled by your former employer.
However, we would like to point out that if you continue to work in Slovakia and at the same time work in another Member State, or other EU Member States, it is necessary to inform the relevant branch of the Social Insurance Agency about this fact by means of a request to determine the applicable legislation, if your residence is located on the territory of the Slovak Republic.