Being involved professionally in transport developments in both South & West Yorkshire, I am aware of several things moving forward - my comments here however are my own views and don't necessarily match up with documents and discussions that I've had !
There needs to be a step change in linkage to the HS2 station at Meadowhall, primarily from western suburbs of Sheffield but also from Barnsley & Doncaster, the MML is due to be electrified in the next control period to Sheffield, it doesn't take a genius to realise that Sheffield to the ECML will come soon after, so I'm seeing an opportunity to run a Chesterfield-Dore-Sheffield-Meadowhall-Rotherham-Swinton-Doncaster EMU service. Currently services through Rotherham and Barnsley are very poor, so again, it doesn't take a genius to imagine a more frequent service between Meadowhall and Barnsley/Rotherham/Swinton etc.
What about CrossCountry services ? I'd expect alternate services in the hour stopping alternately at Sheffield and Meadowhall, perhaps both ?, perhaps even moving from a 30 minute to a 20 minute even possibly a 15 minute frequency using cascaded 221/222 units from the electrified Midland Mainline.
What about ECML services ? I'd imagine that Meadowhall could become a key hub for services to the north, with IEP services complimenting HS2 classic comparable services going onwards to York and Newcastle. Remember that ECML south of York will become much less of a intercity service as passengers will predominantly shift to HS2.
TransPennine ? Currently an hourly frequency, we could see a 30 even 20 minute frequency splitting to new destinations such as Lincoln via Doncaster Robin Hood Airport - although a big increase in passengers is required, which could come if extra runways at Heathrow and Gatwick don't happen.
East Midland Trains - services to Sheffield will reduce significant, I'd see Meadowhall as the new terminus for London trains and a turnaround station for the Liverpool-Norwich service too
A lot is been pinned on tram-train - I can see them working on journeys up to 15 miles, but feel heavy rail is still the solution for longer distance.