There is a way you could do it.
Add Rory Burns to an international squad. Select to use him as a star player.
When you start playing, decline any opportunities you get to play in say, the IPL or any international games, then make sure you accept an English County spot once they become available.
Sign for Surrey in all formats, or the formats you want.
Maybe best not to use a team that has Winter games before the English summer starts, so perhaps put Rory Burns in someone like Zimbabwe's team. Unless of course you have a plan to eventually get him into the England team? In which case you'd need to put him into the England squad and sim the winter. Should take you 5 minutes tops from the Calendar screen once you're in Career mode.