Lannister General

A Lannister general plans an expedition to Winterfell with Ser Jaime Lannister, to fight in the Great War.

Background
He is a high-ranking man-at-arms in service to House Lannister, likely a veteran of the War of the Five Kings due to his age and status.

Season 7
The general and his men are being briefed by Jaime Lannister in the Red Keep. He leaves when Queen Cersei enters the room. Cersei then explains to Jaime that the Lannisters will not be going north, as their pact with Daenerys Targaryen and Jon Snow was a lie, but Jaime leaves anyway. It is unknown whether the general still executed Jaime's plan.

In the books
In the A Song of Ice and Fire series, this character does not appear and has no equivalent.