Are you kidding me? Of course there would be an agency to try to monitor and control instances of time travel. That sort of technology would be incredibly dangerous.
Which is why I think there wouldn't be any agency. The technology is so dangerous, that I think, if it would really work, there would be some maniacs travelling back in time and changing history to their liking. Of course they'd get rid of any such agency first.
I agree with NCC-1701.
Its one thing to investigate the technology and arrest those who are not permitted to conduct that research like stem-cell/cloning research today. You could also arrest due to manipulating a single particle timeline change like in Voyager
's "Year of Hell" episodes.
Its another thing to try arresting after the technology has been invented like NCC-1701 said about the offender "they'd get rid of any such agency first."
Its too delicate of a subject that we may have already had before, that's before this thread's history was changed in the timeline. Its too elaborate and complex to canonize as an official starfleet department. Besides, who is starfleet to tell someone what to do with their own history if it doesn't have a ripple effect?
Better off left alone or in non-canonized literature. IMHO.