Zappe started eight games for New England over the past two seasons. The 25-year-old signed with the Chiefs after being released by the Patriots this summer.
Zappe gives the Browns some protection behind Thompson-Robinson and Jameis Winston, who could start this week against Baltimore.
Coach Kevin Stefanski said Monday he was awaiting more medical information on Thompson-Robinson, who was Cleveland's No. 2 quarterback for the first time on Sunday. He completed 11 of 24 passes for 82 yards and two interceptions before getting hurt.
Thompson-Robinson made three starts last season as a rookie when Watson was hurt. The Browns wound up starting five quarterbacks, with Joe Flacco leading them to the playoffs after signing as a free agent.
Watson is scheduled to have surgery this week after rupturing his Achilles tendon on a draw play in Sunday's 21-14 loss to the Bengals . It's the second straight season he has suffered a major injury after breaking his right shoulder after six starts a year ago.
Watson's career in Cleveland is at another crossroads. The Browns signed him to a $230 million contract in 2022 and he's scheduled to make $46 million in each of the next two seasons.
But Watson hasn't lived up to his contract or expectations and is now dealing with an significant injury that will require months of recovery time.