To get I(ndefinite)LR you have to be here for 6 or 10 years, but it's not quite obvious how and on what status you would bridge that 3-to-7-year gap.

For work visas (and many other cases) it's five years before being able to apply for ILR.

According to this:

If they subsequently qualify for leave under the future immigration system in a route that leads to settlement (indefinite leave to remain) here, an EU citizen who spends time in the UK with a Euro TLR immigration status will be able to accrue that time towards the qualifying period for settlement.

So, to bridge the gap you need to qualify for a work visa, rich person visa, etc., that leads to settlement (so not student visa, for example). I imagine this was deliberate, to make sure that EU citizens who don't meet the income, etc, limits can't become citizens.

You'd have to bridge this gap using the not-yet-determined future visa system. Previous white papers suggest this is like the current one but slightly less strict (lower skill requirements, no resident labour market test), but that was a May government publication.