Joining the academy at hometown club Norwich City at the age of nine, Jed progressed through the ranks to sign a professional contract at the age of 17.
He joined League One Yeovil Town on loan ahead of the 2011/12 season and made his professional debut against Brentford on the opening day of the season.
Making 14 appearances for the Glovers, he returned to Carrow Road that October and his senior bow for the Canaries came in an FA Cup third round victory at West Bromwich Albion in January 2012.
A further loan spell followed at Cambridge United before he signed for Aston Villa on a permanent deal in 2013, making his debut in a League Cup win against Rotherham United.
During his time at Villa Park, further loan spells have been spent in League One at Doncaster Rovers, Yeovil Town and Charlton Athletic, while he also spent the 2015/16 in the Championship at Huddersfield Town, making 38 league appearances.
Jed made 19 appearances in 2018/19 as Villa won promotion to the Premier League, including an appearance in the Play-Off final victory against Derby County. He made his top flight bow against Wolverhampton Wanderers in November 2019.