To summarize, a useful tool they can use and disavow if necessary.
At the beginning of the series he's a thief, having stolen a TARDIS. When they track him down (in The War Games) he's captured, forced to regenerate, and exiled to Earth. But even then they're placing him where they know he'll be needed - the time period they place him in is due to experience some major alien interaction, and they know he'll be able to help.
Almost immediately they begin calling for his help- letting him know The Master is headed for Earth, the occasional taking control of his TARDIS to place him where they need him, etc. Also, if you're a believer in the "Season 6B" theory, the Time Lords even used the Second Doctor as a glorified errand boy, as seen in The Two Doctors and arguably in the contemporary comics.
He's held the position of Lord President for an indeterminate period of time - he either abdicated or was stripped of the title, but possibly not - it tends to change from story to story. even in The Five Doctors his cooperation is somewhat begrudging on both sides.
By the time of Heaven Sent / Hell Bent, after the events of the Time War, he's seen as an absolute hero. The military literally and figuratively switch to his side, supporting him against the Lord President Rassilon.