Not enough time has been allowed.
The Scarborough-York train may be delayed, but assuming it's on time 7 minutes is fairly tight to get from platform 4 to platforms 9-11 with luggage etc.
The XC service is timed as follows:
York 1045 [probably platform 9]
Leeds 1108-1111 [probably platform 12]
Wakefield Westgate 1122-1123
Doncaster 1141-1145
Sheffield 1211-1218
Chesterfield 1230-1231
Derby 1249-1251
Birmimngham New St 1403-1412
(and so on...)
The Scarborough-Liverpool train is timed as follows:
Scarborough 0948
Seamer 0953-0953
Malton 1011-1011
York 1038-1040 [almost certainly platform 4]
Leeds 1104-1108 [almost certainly platform 16]
Huddersfield 1125-1126
Stalybridge 1143-1146
Manchester Picc 1205
(and so on...)
There is a train from Man Pic at 1227 to Birmingham arriving 1358 which is a valid connection on to your train to Exeter, so to get the train you are getting from Scarborough and to end up in Exeter at the same time, if you had not already booked I would say book Scarborough-Manchester (TPE) plus Manchester-Exeter (XC) AP singles and using the XC website for 25% off their leg, but booking it all in one transaction.
It's normally quicker via Derby but there are several diversions that make the XC train between York and Birmingham rather slower than normal.
If you miss the 1045, then what I would do is stay on to Leeds* and give it a try there. If you can see that you have missed it, then stay on to Manchester*.
* Have a word with your TPE guard - most are very friendly I find - preferably before departure, and explain you have a tight connection at York and that you may require to purchase an additional York-Leeds ticket, and possibly an additional Leeds-Manchester ticket on top, and if this occurs, can you use your Railcards to buy discounted off peak tickets on board. If you ask before departure, you have the best chance, or if this is not possible, ask before York and you still have a good chance. The worst the guard can do is say "no" in which case you can get off at York and buy new discounted tickets to Exeter from there.
Changing at Leeds will be busy but the walking distance is probably a bit less. If you do miss it at York, then exit the train at Leeds from the front carriage but not the front doors, use the 2nd doors from the front, or alternatively use the front doors in the 2nd carriage. Then go up the stairs/lift to the footbridge and then down onto platform 12. Platform 16 to 12 is not far. The steps take you down to 12b, and the train is likely to be a bit further toward the (west) end of the platform, at 12a, so you will need to turn back on yourself when you get down the stairs (unless it's a double Voyager or HST).
If you ask again the day before the trip, we can check booked platform numbers and it may be possible to check the train formations too.