Robett is the brother of Galbart Glover, the Lord of Deepwood Motte. He succeeded him after Galbart's death in the War of the Five Kings.
"Yes, my family served House Stark for centuries. We wept when we heard of your father's death. When my brother was Lord of this castle he answered Robb's call and hailed him King in the North! And where was "King" Robb when the Ironborn attacked this castle? When they threw my wife and children in prison and brutalized and killed our subjects? Taking up with a foreign whore... getting himself and those who followed him killed. I served House Stark once, but House Stark is dead." ―Lord Robett Glover responds to Jon Snow and Sansa Stark's plea for help.
Jon Snow, Sansa Stark, and Davos Seaworth secretly meet with Robett to try and gain his support against House Bolton. He refuses to help, as they have only secured the loyalty of House Mormont, and citing that Jon Snow has joined forces with wildlings, whereas the Boltons helped him take Deepwood Motte back from the Ironborn who had captured it and terrorised Robett's family and subjects. Robb Stark, to whom House Glover was sworn, gave no such help (though in all irony, this was Robb's original intention, but he was persuaded otherwise by Roose Bolton). Despite their protestations, Robett refuses to declare for them, and sends them away empty-handed.
Robett, along with other Northern lords, travels to Winterfell following its capture by Jon, where he and the others are berated by Lady Lyanna Mormont, who did offer help to the Stark cause. Robett is the second lord, after Wyman Manderly, to declare Jon King in the North. He apologises for not participating in the battle, and pledges his allegiance to House Stark and Jon Snow.
Along with the rest of the lords of the North and the Vale, Glover meets with the King in the North to plan for the coming war against the White Walkers. When Jon states that all Northerners will be conscripted, Glover initially objects to the idea of women being trained for warfare but comes around to the idea after Lyanna Mormont explains her support. He supports Jon's decision on pardoning Alys Karstark and Ned Umber.
He is later present when Jon convenes another meeting at Winterfell. There, Robett reads Samwell Tarly's letter regarding the vast amount of dragonglass and is informed of Daenerys Targaryen's letter regarding the fact that it would be wise if Jon would bend the knee. Despite the wishes of Robett and other noble lords, Jon still departs Winterfell, leaving Sansa in control of the North.
While Jon Snow is preoccupied on Dragonstone with Daenerys and mining the dragon glass, Lord Glover and Lord Yohn Royce propose that the Regent Sansa take over as ruler of the North. Sansa rejects their proposal and stresses that she is only a Regent. Sansa's younger sister Arya Stark then suggests killing the troublesome lords but is rebuffed by Sansa.
Arya later observes Lord Glover speaking with Lords Royce and Baelish, prompting her to suspect that Littlefinger is plotting to overthrow Jon.
Robett informs Sansa that Jon's absence has shown his arrogance as a King, stating that Sansa herself should take his place.
Robett Glover refused to grant Deepwood Motte's support to Jon Snow and Sansa Stark's fight against Ramsay Bolton. Having seen the error of his ways, Glover has since bent the knee to Jon, the King in the North.