Do you know the old woman at the gate?

Literal

Gate [gen-の] place [at-に] being old-woman [obj-を] are-knowing-[polite Q-ますか].

いる + 老婦人 — the participial いる ('being') used as a relative clause modifier 'being at the gate.' 老婦人 ('elderly lady, old woman') is a polite/formal word for an elderly woman, more respectful than 老女. 知る + ~ている gives the stative 'be in the state of knowing.'