27-year-old Sinclair was one of Chris Wilder's first signings a year ago, moving from Crawley Town on transfer deadline day as the new Northampton manager looked to make an instant impact on a side that was heading for relegation out of the Football League.
And Wilder says it is a sign of the progress that has been made during that year that Sinclair is no longer part of his plans. The Cobblers boss told the official club website: "He needs to be playing regular football."
Robertson, 31, made 39 appearances for the club after joining at a similar time and leaves with the praise of his manager who called him an 'excellent professional'.
Sinclair and Robertson's fellow new arrival from January 2014, Ricky Ravenhill, also left Sixfields during the current transfer window and has since signed for Mansfield Town.
Update - Sinclair has signed an 18-month deal with fellow League Two side York City.