In a letter to the Chancellor, Coun Carl Les urges that Teesport be given Freeport status now.
Freeports, designated as areas with little to no tax in order to encourage economic activity, are a key part of the Government's post-Brexit plans and are backed by Mr Sunak.
Tees Valley Mayor Ben Houchen is leading a proposal to Government for a Freeport on the Tees.
He believes a Freeport could create 32,000 jobs over 25 years.
Much of North Yorkshire would be in commuting distance for these jobs, he says, and the benefits of the wider economic upturn would extend into North Yorkshire - for example supply chains operating from Stokesley and surrounding areas - argues the County Council.
Coun Les welcomes the forecast creation of jobs and a projection that a free zone could create £2bn of additional annual gross value added.
In his letter to the Chancellor, he writes: “Whilst there will be clear and obvious direct benefits for the Tees Valley, it is my firm belief that these will also be felt strongly in North Yorkshire.
“I am extremely encouraged by these projections and their potential positive impact in North Yorkshire.
"As you will understand more than most, many of those living in North Yorkshire have jobs located in the Tees Valley and the boost a Freeport would provide for industries around the port and in the extensive supply chains would be a very welcome boost to jobs in the North Yorkshire area.
"As we emerge from the coronavirus pandemic, creating good-quality, well-paid jobs is going to be critical and this is an ideal opportunity to begin this progress.”
He urges the Chancellor to act now to grant Freeport status to Teesport, rather than to wait until other ports are ready to compete for the status.
Coun Les said: “Once the criteria have been drawn up and have been set out, I believe that the awarding of Freeport status for Teesside could be accelerated as its proposal would comfortably meet the necessary demands.
"Once the other areas across the country reach the stage Teesside is currently at, they would compete for the remaining spots using the same criteria. By taking this approach, Government can accelerate this job creating policy in a fair and appropriate manner.
“As we navigate our way through this economic recovery, we cannot waste time and it seems logical to take this approach to the roll-out of Freeports.”
Tees Valley Mayor Ben Houchen added: “A Freeport on the River Tees would could mean tens of thousands of jobs for people in the Tees Valley and in North Yorkshire.
"I am pleased to be working with Carl Les and his officials at North Yorkshire County Council to make this ambition a reality for both of our areas, because we both know the economy doesn’t stop at county boundaries.
“It is really encouraging that Carl is calling for Freeport status for the Tees to be granted now, we have the land and the plan ready to start work straight away while similar projects in other areas could take years.”
The Treasury has been approached for a comment.