Hi David,
You should actually change it after 3 months in the country
Once the Uk leave the EU, you will need an international drivers license to drive in Europe.
It is easy to get it exchanged for a Slovak one and if you are planning on staying in Slovakia after Brexit then I strongly advise it. You need to go to the Okresný úrad on the corner of Watsonova and Komenskeho street. There is a number/ticket system and, if you need help, the person on the machine usually speaks english so can press the right button for you. The person on the desk may or maynot speak English but they can usually call someone to help out.
Hope this helps,
Denise