late 13c., "bright," from Old French cler "clear" (of sight and hearing), "light, bright, shining; sparse" (12c., Modern French clair), from Latin clarus "clear, loud," of sounds; figuratively "manifest, plain, evident," in transferred use, of sights, "bright, distinct;" also "illustrious, famous, glorious" (source of Italian chiaro, Spanish claro), from PIE *kle-ro-, from root *kele- (2) "to shout" (see claim (v.)).
The sense evolution involves an identification of the spreading of sound and the spreading of light (cf. English loud, used of colors; German hell "clear, bright, shining," of pitch, "distinct, ringing, high"). Of complexion, from c.1300; of the weather, from late 14c.; of meanings or explanations, "manifest to the mind, comprehensible," c.1300. (An Old English word for this was sweotol "distinct, clear, evident.") Sense of "free from encumbrance," apparently nautical, developed c.1500. Phrase in the clear attested from 1715. Clear-sighted is from 1580s (clear-eyed is from 1529s); clear-headed is from 1709.
late 14c., "to fill with light," from clear (adj.). Of weather, from late 14c. Meaning "make clear in the mind" is mid-15c., as is sense of "to remove what clouds." Meaning "to prove innocent" is from late 15c. Meaning "get rid of" is from 1530s.
Meaning "to free from entanglement" is from 1590s; that of "pass without entanglement" is from 1630s. Meaning "to leap clear over" is first attested 1791. Meaning "get approval for" (a proposal, etc.) is from 1944; meaning "establish as suitable for national security work" is from 1948. Related: Cleared; clearing.
To clear (one's) throat is from 1881; earlier clear (one's) voice (1701). To clear out "depart, leave" (1825), perhaps is from the notion of ships satisfying customs, harbor regulations, etc., then setting sail. To clear up is from 1620s, of weather; 1690s as "make clear to the mind." Clear the decks is what is done on a ship before it moves.
"quite, entirely, wholly," c.1300, from clear (adj.).
To go away: let's clear off after graduation (1816+)
To earn a certain amount of money after taxes: cleared 100 Gs