While a direct sequel with the original cast is unlikely, there is "industry chatter" regarding the future of the Barsoom IP:
Carter would wake up back on Earth in his funeral suit, beginning his desperate search for a way back to Barsoom (Mars) to save his family. Why the Original Sequel Was Shelved Financial Loss: filmyzilla john carter 2
A sequel to the 2012 film John Carter has not been officially released or greenlit by Disney, despite persistent rumors and fan-made concept trailers suggesting a 2025 or 2026 release. The Status of John Carter 2 Official Cancellation: While a direct sequel with the original cast