England had been bowled out for just 275 in their first innings, with Tim Southee taking 6-43, in reply to New Zealand's 378 featuring debutant Devon Conway's 200.
"We are also incredibly excited to welcome Afghanistan to our shores for a historic first Test match against Australia," said Cricket Australia's interim CEO.
England lost early wickets, including skipper Joe Root for five, to slump to 30-3 before Stokes put on key partnerships with Jonny Bairstow, who made 28, and Pope.
Babar Azam led Pakistan to a 2-0 sweep over the Proteas in Rawalpindi on Monday in a hard-fought 95-run win on the fifth and final day of the second Test.