The sequence – which was brought to life using animated storyboards and a voiceover by Arthur Darvill (Rory) – was written by Chris Chibnall but never shot.
‘P.S. What Happened to Brian and the Ponds’ was released today on the official Doctor Who website.
Doctor Who executive producer, Caroline Skinner said: “We’re delighted we can present this lovely scene written by Chris Chibnall.
“People took Rory’s dad, Brian, to their hearts very quickly, so it’s fitting we can give the character a degree of closure in this poignant piece.”
The four-and-a-half minute segment offers a glimpse into what became of Rory and wife Amy (Karen Gillan) after they were sent back in time by the Weeping Angels and also features Rory’s father Brian (Mark Williams).
Doctor Who returns to BBC One this Christmas.