Beckett is one of the NPC Allies that you can recruit in Fallout 76 Wastelanders DLC. You do this by completing the quest Narrow Escape. This Fallout 76 Wastelanders Ally: Narrow Escape walkthrough will detail the complete quest that recruits Beckett.
Fallout 76 Wastelanders Ally: Narrow Escape
This quest is threefold; Rescuing Beckett from the prison, retrieving his belongings and building a bar from him at the Camp to finally recruit him.
You will get this quest after you reach level 20. While you’re roaming in the west, you’ll get the task of rescuing a prisoner from the Blood Eagle Prison; the prisoner being Beckett.
The prison is located in the Rollin’s Labor Camp near the south-western end. You’ll find a giant crane there; the prison is inside that crane.
There’ll be a lot of enemies spanning the area, so it’s advisable that you approach the crane prepared for the worse. Take care of all the enemies before approaching…