Mike Shula is a veteran coach who has head coach for the University of Alabama from 2003 through 2006 but has made a number of stops throughout the NFL. He has been offensive coordinator for three teams (Tampa Bay Buccaneers from 1996-1999, Carolina Panthers from 2013-2017, and New York Giants from 2018-2019).
He also has been quarterback coach with five teams (Dolphins, Jaguars, Panthers, Giants, and Broncos). Shula has been with the Bills the past two seasons as a senior offensive assistant.
It seemed like the Bills brought Shula in to help guide Dorsey, who at the time had no experience calling plays, and he might be able to serve a similar role for Joe Brady. However, that doesn't seem as critical and it would make sense for him to at the very least be considered for a quarterback coach position with another team.