Jetes general manager John Idzik isn’t kidding when he promises to give Mark Sanchez plenty of competition this fall. A day after word leaked of the Jets’ interest in Brady Quinn, Idzik kicked the tires on another veteran quarterback when he brought in David Garrard for a workout. The look-see, confirmed by a league source, was necessary because the 35-year-old former Jaguars passer hasn’t played in the regular season since 2010 because of surgeries on his back and knee. On track to be the Dolphins’ starter coming out of preseason last year, Garrard was released in the wake of knee surgery that kept him from being signed elsewhere last season. Garrard, who was drafted by Giants coach Tom Coughlin in Jacksonville in 2002, appeared in 86 games for the Jaguars before being abruptly released before the 2011 season after the team used a first-round pick on Blaine Gabbert. The veteran Garrard has completed 62 percent of his passes for 89 touchdowns (with 54 interceptions) in his nine-year career, compiling an 85.8 rating along the way and leading the Jaguars to their only playoff victory of the post-Coughlin era. Garrard won’t be the only bargain-bin quarterback Idzik and the Jets take a close look at this offseason. Gang Green’s new boss made that clear at his introductory press conference in January and again last week at the NFL scouting combine in Indianapolis. “Everyone, Mark included, recognizes that he, our offense — shoot, our team as a whole — has to perform better than we did in 2012,” Idzik said at the combine. “We’re going to do that. We’re going to do everything to increase the competition so that he plays better.” That competition certainly isn’t on the roster at the moment. The Jets’ current quarterback depth chart is Sanchez, Tim Tebow, Greg McElroy and Matt Simms, and Tebow is expected to be released during the offseason. ESPN reported earlier this week that Idzik is interested in signing Quinn when the former Chiefs quarterback becomes an unrestricted free agent next month, in part because new Jets quarterbacks coach David Lee likes the former Notre Dame star.