An Etymological Dictionary of the German Language/klimmen
klimmen, vb., ‘to climb,’ from a MidHG. klimmen, klimben, OHG. climbun, str. vb., ‘to climb, mount’; corresponding to AS. climban, E. to climb. The nasal was orig. a part of the pres. stem; it did not belong to the root, as is proved by OIc. klífa, vb., ‘to climb.’ As to the identity of klimban with OTeut. klîban, ‘to cleave (to), hold firm,’ comp. kleiben; hence klimmen is prop. ‘to adhere.’