stretch, singing girl, geisha, prostitute
妓 centers on a woman who performs or entertains, historically a singing girl, geisha, or prostitute. The older meaning 'stretch' is likely a separate, rare usage.
妓 combines 女 (woman) with 支, which likely contributes the sound and may relate to skill or performance. The exact historical development of the 'stretch' meaning is uncertain.
A woman 女 beside 支, which looks like a hand holding a branch, suggests a performer using props or gestures. Picture a singing girl or geisha entertaining with graceful movements.
For ギ, imagine a geisha (ぎ) performing: the first sound of 'geisha' is ギ, and the kanji itself means geisha.
maiko; apprentice geisha (in Kyoto)
geisha
(the most thrilling relationships for a man are) another man's wife, a maidservant, a mistress, a prostitute, and finally his own wife
famous geisha; talented geisha; beautiful geisha
geisha
pimp; brothel tout
brothel
kisaeng (Korean female entertainer)
brothel
prostitute; harlot
favored geisha; beloved geisha; geisha someone is showing favor to
woman who earns her living by entertaining with song, dance and playing the shamisen; geisha who sings at parties
geisha; woman who entertains (e.g. by playing the shamisen) for her living
beautiful maiko or geisha
aged geisha
being entertained by a maiko (geisha apprentice)
geisha and prostitutes
ordinance liberating all geisha and prostitutes (1872)
geisha and maiko
child geisha; geisha apprentice