On 29th of March 2019, the United Kingdom will leave the European Union. The Brexit has consequences for all Britons residing in the Netherlands.
There has been made a transitional arrangement by the Dutch government. Britons and their relatives who legally reside in the Netherlands before the Brexit on 29 March may, in case of a no deal Brexit, expats can stay in the Netherlands for at least another 15 months. The transitional arrangement also applies to family members of British citizens who do not have EU nationality themselves. Expats will receive an invite of the IND to submit an application for a definitive residence permit that is required after the transitional period. British citizens are eligible for this permit if they meet the same residence conditions that apply to EU citizens.
The website of the IND updates their content regularly when having an update. You can check the below link for more information:
https://ind.nl/en/Pages/Brexit.aspx