WIll the draft be reinstated if/when North Korea starts WW3?
Historically the greater proportion of Armies of both sides involved in WW1 &WW2 were citizen soldiers drafted as required by their respective countries. The French in the 19th century were heavily dependent on conscripts and until recently some Europeon countries have maintained conscription. There is no doubt should the scenario your question suggests come to fruition the draft will be reinstated. We must all hope this never happens!
With a Democrat in office, it is very likely. Voluntary enlistment under Democrats is usually small, which explains why every time a draft has been instituted…a Democrat instituted. Under Republicans, voluntary enlistment is more than enough to keep the ranks filled. Sometimes, they even have to turn people away or convince them to take a different job in the branch of their choice because of how full it is.
If a law to reinstate the draft or conscription is pushed through parliament or congress then it will be so. But the military do not have the readiness to give basic training to all service-age males, so it is unlikely. But then dear questioner, you could sign up yourself and avoid the tension of waiting. Bet you wont, though!