Carl said: "I am really glad to sort out my next two years with a club that is wanting to match my ambitions and move forward, especially now I have a settled management team in Ian Clark and Nicky Ward.
"I am looking forward to the next couple of years to see if we can bring some silverware to Marske. I would like to thank the committee and chairman who have put this deal in place."
Jarrett joined Marske in the summer of 2014, having previously been at Billingham Town. He helped Marske shock north-east football by winning the league title in his first season, and followed that up with a 2nd place finish the following year.