Something that doesn't get mentioned much is the North Yorkshire Dales...

Kirkby Lonsdale Coaches have taken on former Pennine service 580 (Skipton - Settle) commercially as an extension of their 581 service from Kirkby Lonsdale. A new timetable can be found on the Dalesbus website here
A new addition to service this new route is former Trent Barton Optare Excel Y251DRC

Other increases have been implemented on NYCC's own services too, 14 (Skipton-Embsay) now runs hourly all day, while 211 (Skipton-Malham) now runs every weekday with the introduction of services on Tue/Thu. Service 58 (Skipton-Giggleswick) is replaced by KLC service 580 as mentioned above.

Meanwhile, in South Yorkshire...
A number of service changes were implemented in the Rotherham area on 19th July, as a result of the new "Rotherham Bus Partnership" - A few notable changes as a result of this:
Powells gained a new service 4 between Bramley, Rotherham and Meadowhall
First service 22 between Rotherham and Barnsley now runs every 15 minutes but has been extended half hourly from Rotherham to Meadowhall, and these journeys are numbered as 22M
TM Travel service 31 (Rotherham-Meadowhall) was doubled to half hourly, and now also has 2 branded buses - 1193/4 (YJ57EHB/EHC) have been repainted out of "Travel South Yorkshire" livery into a new yellow Line 31 livery - as seen here on YJ57EHC
TM Travel service 271 (Crystal Peaks - Worksop) has been culled and replaced with a 2-hourly (in each direction) loop within South Yorkshire operated as service 26/26A
TM Travel service A1 (Sheffield - Rotherham) has been mostly cut, now running between Meadowhall and Waverley only, the rest has been replaced by various services, First services 71 (Rotherham - Meadowhall via Brinsworth & Sheffield Business Park) and 72 (Sheffield - Rotherham via Catcliffe & Brinsworth)