Tully Deck (my edit of SwordofMorning's Tully League Deck on Cardgamedb)

House (1)
House Stark (Core) x1

Agenda (0)
N/A

Plot (7)
Storm of Swords (LoW) x1
Twist of Fate (APS) x1
Respect of the Old Gods (LoW) x1
A City Besieged (CD) x1
Into the Lists (TftH) x1
Family, Duty, Honor (LoW) x1
Take Them by Surprise (LoW) x1

Character (30)
Knight of the Red Fork (LoW) x3
Riverrun Messenger (LoW) x3
Hoster Tully (LoW) x2
House Tully Septon (LoW) x3
Hodor (Core) x1
Guard at Riverrun (LoW) x3
The Blackfish (LoW) x3
Trident Reinforcements (Core) x1
Edmure's Host (LoW) x2
Ser Edmure Tully (LoW) x1
Catelyn Stark (LoW) x1
Knight of the Tumblestone (Core) x1
Ser Rodrik Cassel (Core) x1
Meera Reed (TftH) x1
Damon Dance-For-Me (VD) x2

Brienne of Tarth (PotS) x2

Location (17)
Great Keep (Core) x3
Frozen Outpost (LoW) x2

Godswood (LoW) x2
Lord Eddard's Chambers (LoW) x2
Narrow Sea (Core) x2
Northern Fiefdoms (Core) x3
Street of Steel (LoW) x1
Riverrun (LoW) x2

Attachment (3)
Poisoned Coin ( THoBaW ) x3

Event (10)
Distinct Mastery (Core) x2
Die by the Sword (LoW) x3
Routing the Charge (LoW) x2
Endless Endurance (LoW) x3

I am a new player and this is my first attempt at a deck for AgoT LCG. I currently own the following:

Core Set ~ LoW House Set ~ PotS House Set

RoW – DB – FtC – TftH – APS – VD – CD – AHM – THoBaW.

I was told Maege Mormont in HM could work well but thought Brienne and Damon had more to offer plus their immunities were valuable.

I also considered Support of the Kingdom instead of Routing the Charge but I only have one Core Set so far so limited number of copies of that and likewise Trident Reinforcements and Knight of the Tumblestone .

Also, would an additional Catelyn Stark be useful or a dead card?

Really, you need a bigger cardpool before you can do much serious deckbuilding. For example you use die by the sword but you only have 5 war crests. I would suggest starting with more core sets. It may seem like a waste to get more copies of a card you already have, but it's going to be necessary if you intend to keep playing (and especially if you plan on using die by the sword still since you will need more KotT then). The only suggestions I can make right now are Valar Morghulis over ACB (because it's your only city plot, it can only kill 0 cost locations, which is not very useful) and to give Lethal Counterattack a try.

It is true, I need to build up my card pool more AND get at least a second Core Set. I did change that deck a bit and replaced A City Besieged with Building Season. Thank you for the time to consider my post and your advice.