老妓 is read as ろうぎ (rougi) and means aged geisha.
ろうぎ
rougi
ろうじゃく
young and old
ろうじん
old person
ろうご
old age
ろうか
ageing
しにせ
long-established shop
おいる
to age
ろうじゅう
member of shogun's council of elders
ろうじゃくだんじょ
men and women of all ages
ろうし
Laozi
ろうば
old woman
ろうじんほーむ
retirement home
ろうねん