The IND has created a special webpage concerning Brexit and the rights of residence in the Netherlands for UK citizens. We have reprinted part of this information below from this link: https://ind.nl/en/pages/brexit.aspx
On 29 March 2017 the United Kingdom has announced to withdraw from the European Union. This exit (Brexit) will take place on 29 March 2019 and has consequences for British citizens and their family members who wish to continue living in the Netherlands. On this page you can read more about these consequences. This page will be adjusted in case of developments.
At this moment the United Kingdom (UK) and the European Union (EU) are negotiating the withdrawal agreement in phases. You can read information about the process of negotiating and interim agreements on the website of Government of the Netherlands.
The UK will remain an EU-member state until the Brexit. This means that you will remain an EU-citizen to that date. What your residence rights will be after this date, depends on the outcome of current negotiations. However, there is a provisional agreement about the rights of British and EU citizens after the Brexit. The European Commission has drawn up a document with frequently asked questions about the provisional agreement.
What can you do?
The negotiations between the UK and the EU are still in progress and the withdrawal agreement is not final yet. That is why the IND cannot say what you must do in order to stay in the Netherlands after the Brexit. The IND can tell you what the provisional agreement means for you as a British citizen in the Netherlands after the Brexit. And what voluntary options you have today as an EU citizen to regulate your stay.
Please follow the links for the full information for your situation.