Clearly Nottingham will gain from HS2 as the home to station journey doesn't really change that much, perhaps improves with on site parking, but worse for tram users with the extra leg out to Toton... Derby will suffer to a degree pushing users to cars for the home to station part but will perhaps gain on a more regional level with clearing some express units out, Leicester stands to gain in my eyes, as the passengers north of there heading to London will mostly transfer, leaving more room for express and semi-fast services...
Depends where you live. For most people in the western part of Nottingham the HS2 station will be ideal for London journeys whether accessed by tram, car or any bus service that might appear. There are significant time savings on HS2 to Birmingham, Leeds or beyond, or Heathrow, so this will be the preferred rail choice for much of Nottingham.
However for central, eastern and some other parts of the Nottingham conurbation the Midland station will remain far more accessible especially by public transport. Importantly this includes the city centre, which will be a primary destination for inward visitors. Unless deliberately decelerated the fast London-Nottingham service on the MML will be around 90min by then, with scope to remove calls at Market Harborough (stop transferred to a new fifth Leicester train) or East Midlands Parkway (primarily a park and ride for London, so Toton will take most of its market and a fast London service would no longer be worthwhile). With HS2 offering a 53min London to Toton time the tram is simply too slow for central Nottingham and unless there is a fast heavy rail link with really slick connections there, the time saving via Toton won't be enough to make it worth the hassle of changing trains.
Much of the above applies in mirror image to Derby too, minus the benefit of the tram and noting that Toton to Nottingham is mostly urban but Toton to Derby is mostly rural so there is less catchment that side for HS2.
Leicester-London will gain nothing from HS2 so there will be an imperative to maintain a service at least as fast as today's, and a 125mph straight EMU or a bi-mode could shave off a few minutes. As these might as well continue to Derby, Nottingham or Sheffield and there are a limited number of places worth stopping at in between, then it is likely all the East Midlands cities would have London times via the MML at least as good as today's.