We caught a glimpse at Yeti’s employment with Monsters Inc. at the end of the prequel, Monsters University, when he introduces Sulley and Mike to their new jobs as mail sorters.
You can hear him hint at how he will eventually get himself banished in in his advisement to the duo to never peek at the mail.
John Ratzenberger’s role comes into play when Waternoose (James Coburn) banishes James “Sulley” Sullivan (John Goodman) and Mike Wazowski (Billy Crystal) to the Himalayas, where they meet Yeti, who treats them to snow cones in his cave.