Bethell had impressed for England in his debut series against New Zealand when he scored three half centuries, including a knock of 96, when batting at number three.
But vice-captain Pope, who played as a middle-order batter in that series, is set to be promoted to number three after his knock of 171 in the one-off Test against Zimbabwe.
Bethell had missed the Test against Zimbabwe as he was playing for Royal Challengers Bengaluru in the Indian Premier League.
Meanwhile, all-rounder Woakes returns to the team for the first time since December while Carse, who has played five Tests for England in Pakistan and New Zealand, will get the opportunity to impress on home turf for the first time.
England team
Zak Crawley, Ben Duckett, Ollie Pope, Joe Root, Harry Brook, Ben Stokes (captain), Jamie Smith (wicketkeeper), Chris Woakes, Brydon Carse, Josh Tongue, Shoaib Bashir