The key factors controlling the formation and dynamics of relicpermafrost and the conditions for the stability of associated gas hydrates have been investigated using numerical modeling in this work. A comparison was made between two scenarios that differed in the length of freezing periods and corresponding temperature shifts to assess the impact on the evolution of the permafrost–hydrate system and to predict its distribution and geometry. The simulation setup included the specific heat of gas hydrate formation and ice melting. Significantly, it was shown that the paleoscenario and heat flows affect the formation of permafrost and the conditions for gas hydrate stability. In the Laptev Sea, the minimum and maximum predicted preservation times for permafrost are 9 and 36.6 kyr, respectively, whereas the presence of conditions consistent with methane hydrate stability at the maximum permafrost thickness is possible for another 25.9 kyr. The main factors influencing the rate of permafrost degradation are the heat flow and porosity of frozen sediments. The rates of permafrost thawing are estimated to be between 1 and 3 cm/yr. It is revealed that the presence of gas hydrates slows the thawing of the permafrost and feeds back to prolong the conditions under which gas hydrates are stable.