Season 5 Edit
When we are introduced to Buddy in Nev-AD-a, he is the Nevada Secretary of State. He first meets with the O'Brien and Meyer teams to discuss the rules of the recount. He has a conversation with Amy in Mother, surprised and amused by her language.
Buddy then reappears at the White House Congressional Ball, where he and Amy go home together. While in Nevada shortly before Inauguration day, Amy and Buddy seem to be in a relationship together.
Season 6 Edit
In the sixth season, Buddy and Amy are engaged, and Buddy is running for Nevada Governor in the 2018 elections. Amy is running his campaign. His campaign hits a major snag, however, when he is arrested for DUI, and dashcam footage of the arrest shows him sexually harassing the female cop arresting him, saying things that seem to be thinly-veiled criticisms of Amy, and eventually exposing himself to the police officer.
In the aftermath of the scandal, Calhoun's fiancee, Amy Brookheimer, says in a joint interview on CBS This Morning that she most enjoys spending quiet time with Buddy. After hearing this, Calhoun drops out of the Nevada Governor's race to spend more time with her. She almost immediately leaves him to go back to work for Former President Selina Meyer.