1560s, "action of making clear," from clear (v.) + -ance. Meaning "a clear space" is from 1788. Meaning "approval, permission" (especially to land or take off an aircraft) is from 1944, American English; national security sense recorded from 1948. Clearance sale attested by 1843.
the plane was given clearance to land
cleanse
cleanser
cleansing
clean-up
clear
clearance
clear-cut
clear-cutting
clearing
clearing-house
clearly