Batting still 'main priority' for Pope despite added wicketkeeper duties
Foakes, who missed the opener through illness, fully recovered in time for the second test but England skipper Ben Stokes said Pope would continue behind the wicket.
Pope smashed 60 runs in 61 balls in his second innings in the second test, before pulling off a diving catch as Mark Wood dismissed Saud Shakeel, a wicket which proved costly in Pakistan's 26-run defeat.
"My main priority is to keep churning out runs," Pope told reporters. "I'd still love to tie down number three, make that my own. That will be my primary focus.
"I definitely didn't expect to be keeping out here. It wasn't on my radar ... I've enjoyed the experience.
"I can still do better. I'm not even going to compare myself to Foakesy as a keeper, but I took my chances in the second test."
Pope added that he feels like a player reborn under captain Stokes and coach Brendon McCullum.
"The two guys at the top have helped me grow, not confidence but the freedom to express myself and how I want to play," he said. "It's been great for me, hopefully I keep that consistency."
England, who registered their first series win in Pakistan since 2000-01, play a final match against the hosts in Karachi, beginning on Saturday.