From Old English (before 12th century), from Proto-Indo-European '*glei-' ("to stick, cling, adhere"), from PIE *glei- ("to stick, adhere").
To go or come up a slope, incline, or staircase; to ascend by using the hands and feet.
From Old English 'climban' (to climb, ascend), from Proto-Germanic '*klimbaną' (to climb), probably from PIE root *glei- (to stick, to adhere, to smear). The connection between climbing and sticking makes physical sense — you climb by clinging, gripping, adhering to surfaces. The same root family may include 'clay' (the sticky earth), 'glue,' and 'clamber.' The silent 'b' in 'climb' was pronounced in Old English ('KLIM-ban') and was gradually dropped
The silent 'b' in 'climb' is a ghost of Old English pronunciation — Anglo-Saxons said 'KLIM-ban' with a fully pronounced 'b.' The same phantom 'b' haunts 'comb,' 'lamb,' 'dumb,' 'tomb,' and 'bomb' — all words where the 'b' was once spoken but fell silent, leaving spelling as a fossil record of medieval English sounds.