Cirque Peak is the southern end of the High Sierra in that it is the last of the contiguous chain of glaciated peaks in the Sierra Nevada (Olancha Peak being the southern-most locale of significant glaciation).
The peak is easily reached from either Cottonwood Pass or New Army Pass. Class 1 routes may be followed from south, west, and north. Some class 2 and class 3 terrain may be scrambled along its eastern aspect, and up the actual north face that overlooks the High Lake cirque.
There are excellent views from the summit, similar to those obtained by climbing nearby Mount Langley, but without so much huffing and puffing.
From the town of Lone Pine on Highway US-395, drive 5 miles west on Whitney Portal Road. Go left on Horseshoe Meadow Road and continue 20 miles up a remarkable set of switchbacks to the Horseshoe Meadow trailhead. The peak may be approached by hiking up New Army Pass (as for Mount Langley) or up Cottonwood Pass to Chicken Spring Lake.
For the recommended route, the Cirque Peak Traverse, use the New Army Pass approach, hike across the summit (generally following the Sierra crest), then descend into the Chicken Spring Lake cirque and on to Cottonwood Pass.
For day hikes, no permit required. For overnight stays, obtain a free wilderness permit at the Mount Whitney Ranger Station in Lone Pine. Permits may be reserved in advance for $5 per person.
Mt. Whitney Ranger Station
P.O. Box 8
Lone Pine, CA 93545
Best season is June through November. The Horseshoe Meadow Road climbs to 10,400' and is not passable after the first significant snows, making an approach in off-season a tedious slog, even on skis.
For day hikes, camp at the hiker sites at the Horseshoe Meadow trailhead. For overnight hikes, good camping may be had near Chicken Spring Lake, above Cottonwood Pass, or at South Fork Lakes or Cottonwood Lakes.
You may also camp low at the Lone Pine Creek campground on the Whitney Portal Road, or the Tuttle Creek campground on the Horseshoe Meadow Road. Neither of these options allows for good acclimatization before the hike, so I don't recommend them.