Updating its licences with the Oil and Gas Authority, Third Energy has set out plans which include fracking at its existing well at Kirby Misperton, near Pickering, by the end of this year.
The firm also says it wants to then drill a well a year in Ryedale by the end of 2022, including a 1,000m well which it would frack by the end of September next year and a 3,000m well by the end of September 2021.
According to its updated licence, Third Energy also wants to drill and frack a fourth well in the area by the end of December 2022.
The company still needs to pass the government's financial resilience test before it can get the go-ahead for any fracking to take place in Ryedale.
Steve Mason, from the campaign group Frack Free Ryedale, says: "This reinforces the case we've always been saying, that this isn't about just one well, it's about multiple wells, multiple sites, which could seriously impact Ryedale."