My assessment is that this disclosure of a nuclear powered submarine is more for PR purposes than any actual near term military benefits. This technology is very difficult to master and they are likely many years from having a working prototype. However, like with their nuclear program if nothing is done to reign their program in over a 10-15 year period, they will likely eventually have a working nuclear powered submarine:

North Korean leader Kim Jong-un, third from right, smiles during his visit to a shipyard to inspect nuclear submarine construction in this photo released by the North’s official Korean Central News Agency, Saturday. Yonhap
North Korea has publicly unveiled the construction of a nuclear-powered submarine, a weapons system that could pose a serious security threat to South Korea and allies if successfully developed, due to its ability to operate submerged for months.
On Saturday, Pyongyang’s state-run media, the Korean Central News Agency (KCNA), released photos of leader Kim Jong-un inspecting shipyards focused on constructing warships, including “a nuclear-powered strategic guided missile submarine.”
“Kim stressed the need to make overwhelmingly powerful warships to contain hostile forces’ habitual gunboat diplomacy,” the KCNA reported without disclosing the exact location of the shipyards.
It was the first time that North Korea disclosed the ship’s appearance.
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