The closest trailheads are those for Stein Butte Trail, Summit Lake Trail (at Squaw Lakes), or New London Trail.
Elliott Ridge provides an important link between Stein Butte and Squaw Lakes. Accessed by an assortment of singletrack trails and at least one forest road, it is a scenic trail by itself, or, more logically, part of a longer loop.
The western terminus of the trail is at the top of the New London Trail, which is also the eastern end of the Stein Butte Trail just east of the summit.
If you're like me and have reached this point following Stein Butte Trail, the introduction to Elliott Ridge is a rude awakening, as the trail eschews manicured switchbacks in favor of the direct approach up and over every pitch along the ridgeline.
Thankfully, the steeper grades soon ease, and fun, interesting singletrack leads along the ridge for nearly two miles to where it morphs into doubletrack just west of a place called Mingo Gap.
Continuing along a forest road, the Carlton Pasture trail is soon passed on the right, and a steady ascent leads past the high point of the trail at almost 5000 feet. From here, a half-mile descent brings one to the upper (south) end of the Summit Lake trail.
It is possible to drive to this, the eastern end of Elliot Ridge Trail, via forest roads coming up from Applegate Lake and passing Squaw Lakes.
Recommended options from here are to 1) Down Summit Lake trail past Squaw Lakes and down the gravel road in the drainage to pick up the Payette Trail
along Applegate Lake; or 2) Head back along the ridge westward from whence you came, then descend New London Trail or Stein Butte Trail.