Before beating Father Gascoigne head to the rafters of Central Yharnam, just past the caged Rabid Dogs, to meet her and receive Bold Hunter’s Mark x2 and the Shake off Cape gesture.
After unlocking the Cathedral Ward gate:
After unlocking the Hunter Chief Emblem gate, but before defeating Vicar Amelia, return to Oedon Chapel and head out the back and turn left to find Eileen near the fence for the Shhh! gesture.
You can now head to the Tomb of Oedon, where she will be fighting Henryk. If you decide to help her you’ll obtain the Approval gesture and the Heir Rune off Henryk’s corpse. If you do not help her she will die and her quest line will end, meaning you won’t have access to the Hunter Oath from the Hunter of Hunters covenant, although you can loot the Crow Hunter Badge off her corpse.
After defeating Rom, the Vacuous Spider:
Return to the Grand Cathedral to find Eileen outside for the Wait gesture. If you head inside the Grand Cathedral you’ll have another fight and once defeated you can return to Eileen for the Crow Hunter Badge and the Hunter Oath from the Hunter of Hunters covenant.