Yeah, you can’t actually do anything to the agent, normally you wouldn’t even know he was there; the only way for him to leave is if he does something and fails - then he gets executed.
You can visit Klingon space, like a tourist… do some beard-watching. There’s not really anything you can do there, but… 
And yeah, it’s up to 14 for the Enterprise because of Scotty.
So I couldn’t, say, visit one of the planets in Klingon space and explore it to convince it to join the Federation? (Asking for a friend…)
No, all the planets in the home zones are members/satellites, which cannot be influenced; and of course they’ve already been explored, so you can’t explore them.
Otherwise the Klingons would just go to Vulcan an persuade all the Spocks to join them and then win all the space 
I see. Shame though - let me think on the Enterprise move then.
Takes notes
What about Organia - can I go there with some tea and biscuits and convince them of the cut of the Klingon’s gib?
No, not unless you have a Borg. They’re not very impressed by all this starships business.
I wasn’t offering them starships: just Rich Teas and a quiet word in their shell.
Anyway, so the decision is to go to a new planet, stay put and maybe work on this one, or head to Melkot to put a counter-offer. Hmmm.
Their shell remains tightly closed, not even allowing in the smell of tea. They can replace dilithiums, that’s it. 
And actually Enterprise doesn’t even have a commissioner, so they can’t do political actions anyway.
What about a Klingon starbase? Can I go there and start a mutiny? Through careful dialogue, of course?
sigh. Why couldn’t I just run some Twilight Imperium and let these warmongers fight their way into oblivion?
Discourse says I should “Invite everyone to the conversation” cause I’ve (officially) been talking to you too much. 
Just searching for options. Starting to look a little Kobiyashi Maru already, so exploring the possibilities …
It should be noted that if the ship gets blown up while it isn’t on an explored planet, everyone on it dies. So probably exploring something would be a good idea?
Also, if that happens, it can come back from a starbase, and pick up the crew again without any spies.
I feel we should have swapped roles.
Possibly - but with two ships crippled and the other two under enemy agent control, I’d argue the odds of successful exploration with the “infected” ships is slim. So the Enterprise stays put.
@GabrielH asked for a die roll:
I mean, the Agent doesn’t actually affect anything till the Political phase
But here we go
Ares (5): 2d6: 6 + 3 = 9
Beijing (1): Impulse
Surak (2): Impulse
Enterprise: No movement
Nothing happens. 