Former Mansfield, Hucknall and Gainsborough winger leaves Notts County
Hawkridge joined the Magpies in the summer of 2017 and has gone on to make 44 appearances for the club.
Yet the majority of those came last season and he has been limited in first team opportunities this term.
And the two parties have come to an agreement over a release from his contract to allow him to “pursue an opportunity with another club”.
“Terry leaves with our best wishes,” said Magpies manager Neal Ardley.
“He was sought-after by a few clubs and sometimes you have to take the opportunity to move a player on when it’s in the best interests of both parties.”
Hawkridge had a brief stint at Mansfield Town in 2015.
He made his Football League debut for Scunthorpe United in 2013 and spendt three years with the Iron.
A move to Lincoln City materialised that summer and he played 39 times as the Imps made it to the quarter finals of the FA Cup and promotion back to the Football League.
Hawkridge posted on Twitter: “Just wanted to say thank you to @Official_NCFC for giving me the opportunity to play for a great club. I wish nothing but the best for players, fans and everyone involved with the club. Good luck to the boys.”