Linda Shelby was the wife of Arthur Shelby Jr.
Linda used to be a Quaker (a member of a religious Christian movement). She now helps Arthur with his sobriety in his life, among other things.
Linda attends the wedding of Thomas Shelby and Grace Burgess, and helps Arthur with his best man speech for the wedding. She proves to have a fairly large influence on Arthur, a quality that Thomas has taken to disliking.
She tries to get Arthur to stop 'work' at night for religious reasons, which Arthur does not fully oblige but is seen to compromise, for example after burning a pub for the Blighters he immediately goes home despite John's mockery of him.
Furthering her insistence that Arthur's night work should end, she announces to him that she is pregnant.
Linda becomes troubled after her and Arthur return to Small Heath, she is seen to be using cocaine in episode 6 in the bathroom during the fight night between Goliath and Bonnie Gold.
"Keep his balls empty and his belly full." -- Linda Shelby to Arthur Shelby
"It's not me that's doing the gambling. I'm just taking the bets." -- Linda Shelby to Polly Gray