The long-hinted-at McCartney III album is now listed on Amazon, but there's been no official news release yet from Paul.
Here is the album description from Amazon
Paul McCartney will release McCartney III on December 11th. Paul hadn't planned to release an album in 2020, but in the isolation of "Rockdown," he found himself fleshing out some existing musical sketches and creating new ones. Before long an eclectic collection of spontaneous songs would become McCartney III: a stripped, self-produced solo work marking the opening of a new decade. Built mostly from live takes of Paul on vocals & guitar/piano, overdubbing bass, drums, etc. atop this foundation.
Also online is a McCartney III "333 Edition" vinyl edition from Third Man Records, Jack White's label.
Here's a peek at that:
Here's the description from Third Man:
McCartney III —333 Edition is limited to 333 copies and is pressed on 'yellow-with-black-dots' vinyl created using 33 recycled vinyl copies of McCartney and McCartney II by Third Man Pressing. This special "regrind" pressing, the first version of McCartney's third self-titled solo album available for purchase, is hand-numbered and features an exclusive screen-printed jacket.
Stay tuned for more details!