The 27-year-old has signed a new deal that will keep him at Turf Moor until the summer of 2023.
Pope only made three appearances last season after a shoulder injury derailed his campaign, but the England international wants to turn things around next season.
“I want to get back to where I left off and help the club build on the three years I've had here so far," said Pope, whose existing contract had 12 months left to run.
“Last year was a bit of a non-starter for me with the injury. It was frustrating and didn't pan out as I hoped after such a high the season before.
“But it's been a fantastic time here and I want to help the club to keep moving forward."