The top three meters of arctic permafrost is estimated to contain about 1700 metric gigatons of carbon, roughly twice as much as the whole atmosphere currently contains. There are several factors that effect how this may be released into the atmosphere and nothing is known for certain.
One big possible player is CO2 producing bacteria growing in the top layer of the soil. Icy and soggy conditions inhibit their growth right now, but this could change if things dry out.
One study suggested that 60–120 ppm worth of CO2 could be released by 2200. 120ppm is about the whole amount of extra CO2 released by humans so far.
Robert Henson, The Thinking Person’s Guide to Climate Change, p. 117
Kevin Schaefer, Tingjun Zhang, Lori Bruhwiler & Andrew P. Barrett (2011) Amount and timing of permafrost carbon release in response to climate warming, Tellus B: Chemical and Physical Meteorology, 63:2, 168-180 https://www.tandfonline.com/doi/pdf/10.1111/j.1600-0889.2010.00527.x?needAccess=true