Countess was most recently with Philadelphia, which claimed him off waivers from the Rams in May but waived him in August. He was a sixth-round draft pick of the Eagles in 2016. He was cut before that season and signed with Los Angeles. He had 54 tackles, two interceptions, one sack and three passes defensed in 37 games for the Rams from 2016-18. He also returned kicks last season for the NFC champions, averaging 24.6 yards on 17 returns.
Maulet had two tackles in five games with the Jets this season.
The Jets also signed offensive lineman Corbin Kaufusi to the practice squad, where he'll join his brother Bronson, a linebacker. New York had a vacant spot after Baltimore signed safety Bennett Jackson to its active roster.