This page explains how to complete the level 80 post-Shadowbringers quest "An Old Friend".
This quest is available if you have completed the quest A Sleep Disturbed.
Starting the Quest
Talk to Y'shtola in the Rak'tika Greatwood to begin the quest.
Speak with Runar in Slitherbough
You can either teleport to Slitherbough, or you can go southwest to where the orange arrow is pointing in the minimap. Talk to Runar to proceed.
Speak with Asgeir
Go east from the Slitherbough Aetheryte to the quest icon. Talk to Asgeir to proceed.
Take the Well-Worn Broom to Y'shtola
Go west to go outside, then go southeast to the quest icon. Talk to Y'shtola and hand over the Battered Broom to proceed. There will be a cutscene.
Speak with Thancred
Go northwest to the quest icon on the map and talk to Thancred to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to Y'shtola to accept the next quest: Deep Designs.