it appears that dominic raab will become the prime minister on the event of boris johnson dying. they'll need to prorogue parliament, if it isn't already suspended, but the party has been clear on who it is deputizing, and who it will present to the queen, when she calls on the tories to form the next government.

but, how permanent that position is would up to the tories, themselves. they may choose to have a leadership process immediately after the pandemic is over, or might push it for a bit. but, dominic raab will need to win an election for party leader to remain prime minister, and will be expected by everybody to do so as quickly as is feasible.