As a preface to the exercises listed below, it should be mentioned that the great majority of exercises performed for climbing are bodyweight only, and that while a facility such as ours may offer a wide array of specialized machines, bodyweight exercises demand control from the entire body, the execution of which reflects the full bodied nature of climbing.
Using a pull-up bar, hangboard, or any similar device, pull up above the bar and then, holding this altitude, move from side to side, pushing away with one arm while locking off with the other in an alternating manner. The core should be tight and controlled, letting the legs swing only minimally. The exercise focuses on the shoulders and back, which is beneficial especially in boulder-style sequences moving laterally that rely on upper body strength when the feet either cut or become minimal. See also, iron cross and gaston movement.
Frenchies are an alternate form of pull-ups, being more sustained and involved. From a dead-hang, pull up fully and count to three or five (according to the intensity of the workout), lower, and raise fully again, this time lowering until the arms are half-cocked at 45 degrees (acute angle), hold for time and lower. Repeat, pulling up fully and lowering to both 90 degrees, and 45 below 90 (obtuse angle), maintaining the lockoff count for each. After lowering to dead hang after the obtuse angle, this is 1 rep. Frenchies are a good power endurance workout, maintaining a constant strain over time and multiple positions. This is a staple workout across many disciplines.