Thanks for your response, Missjef.
Your problem getting back to the Harrogate area isn't with the buses and trams. It's with the trains.
The RHCP concert is scheduled to end at 2230 but the last train, which connects at Leeds for the Harrogate branch, leaves Sheffield station at 2221, so you won't be able to get back to Harrogate after the concert.
If you're able to arrange your own transport from Leeds, there are trains from Sheffield to there, leaving at 2315 (arrives 0029) and 2359 (arrives 0101). To connect with these trains, there are trams scheduled from the stadium as follows:
Depart 2234 - Arrive at station 2258 (change at Castle Square).
Depart 2254 - Arrive at station 2318 (change at Castle Square).
Depart 2315 - Arrive at station 2338 (change at Castle Square).
Depart 2335: Arrives at Castle Square at 2346. No connection to the station but you could walk there in time to catch the last train to Leeds.
As has been stated, it's likely that extra trams will run because of the concert and there'll still be buses, to Sheffield Transport Interchange, running past the stadium until well after the concert finishes.
Although it doesn't help to get you home (because there aren't any convenient late services), it might be worth noting that the nearest station to the stadium is actually Meadowhall. If you travelled, from Harrogate or Leeds, to Meadowhall station, the stadium is just 6 minutes away by tram.
Chris