The ECB have a pyramid system a bit like football. League cricket below the county level has various levels, the top of which are the Premier Leagues. There's about 30 of them around the country, 4 In Yorkshire: Yorkshire North, Yorkshire South, Bradford, North Yorks/South Durham. These teams often have county professionals playing when they are not playing for the counties, and overseas professionals. The Yorkshire CC Academy team play in Yorkshire North. It's a very good standard of cricket.
Hull CC were in the Yorkshire North Premier but got relegated last season.
There is a playoff at the end of each season with the winners of each league competing to be Yorkshire Champions (in the case of the Yorks/Durham one its the top placed Yorkshire team). Hanging Heaton (from Bradford) are the current champions.