There is a hard deadline attached to registering as a resident, and it is short enough that people who arrive planning to sort the paperwork later often find it has already passed. The rules split sharply along EU and non-EU lines, with British licences sitting in their own post-Brexit position.
It depends entirely on where your licence is from. With an EU or EEA licence you're fine for years — it stays valid to drive on for as long as the card itself is valid, generally up to 15 years from issue, with no obligation to switch to a Dutch one while you live here. Everything else gets 185 days from the date you register as a resident (your BRP registration), after which you either need to have exchanged it, if your country qualifies, or you're required to take both CBR exams. The UK sits in a slightly different spot post-Brexit: British and Northern Irish licences made RDW's designated exchange list, all categories, no test — so you get the exchange route rather than exams, but you still want it done within that same window rather than let the clock run out.