In The Legend of Zelda: Tears of the Kingdom, you can start The Beckoning Woman side adventure by speaking with Penn at Outskirt Stable during the Potential Princess Sightings side adventure.
Head south from Penn following the main road to find a sad woman (Ralera). Speak with her then head east down the road until you find her again. Make your way up to the top of the cliff she showed you. When you arrive, speak with her again.
Once again you’ll have to find her! This time, glide down to the opposite cliff and speak with Ralera there. This will lead to a fight! Take down the enemy then speak with Penn to complete the quest.