Moving from his native London to Bristol as a teenager, Jennison started life as a footballer with Bristol City, where he joined the Robins Academy in 2002.
After breaking into the first-team at Bristol Rovers, Jennison made over thirty appearances in the 2006/07 season, which saw Bristol City earn promotion to the Championship.
After departing Bristol City, Jennison moved north of the border for spells with Dundee and St Johnstone.
On returning to the Football League in 2011, the winger joined Stevenage, before stints at both Port Vale and Scunthorpe in the third-tier of the English football.
Following a spell with Irish side Sligo Rovers last season, Jennison joined the ranks at Rodney Parade in June on a one-year deal.