The 23-year-old, who initially joined the League One outfit in November, will remain at Brunton Park until January 1.
"I've thoroughly enjoyed the last month because it's been a chance for me to get onto the pitch and get games," Amos told Carlisle's official website.
"I'm delighted that it's been extended because this has been a great move for me.
"The fans have been brilliant with me and we've picked up some decent results along the way. The games come thick and fast over the Christmas period and hopefully I'll do enough to be involved and to help the team even more."
Amos has made four appearances for the Cumbrians.