Tessa Graves is an FBI Agent from the San Antonio office. She has been trying to arrest the entirety of the Rodeo Kings (Crystal West, Clint West, Jaxon Davis, and Twyla Jean) since at least ten months prior (but most likely longer than that). She had been involved in Cordell's previous undercover operation, "Operation: Watch The Throne", in their first attempt at catching the Kings.
She returns in Duke because she believes that Cordell is involved with Twyla again, and that he had stolen $300,000 from the robbery four months prior. Cordell is aware that she thinks he's crooked, even asking her on multiple occasions if she still believes so. Twyla was finally brought to justice by Cordell and Micki (acting undercover as Duke and Adriana respectively), and was arrested by Tessa. Twyla believes Duke (Cordell) was shot and killed by Tessa when he tried to escape capture, but it was all a ruse. Before Tessa leaves, she tells Cordell that she does finally believe he's clean, at least for the Rodeo Kings robbery. It appears she's poking fun, as she gives him a wink a moment later while saying "Well, I wouldn't have shot you if I was gonna cuff you."