Yes. Maybe. Maybe not. These opinions come from, you guessed it, a legal analysis. In spite of my snark, cnn.com does offer both a legal and political analysis of the possible outcomes of a request from Zimbabwe to the U. S. for the extradition of Walter Palmer, the Minneapolis dentist and trophy hunter responsible for the death of Cecil. There seem to be two bottom lines.
As a legal matter
... the courts and even the Department of Justice, under extradition treaties, are little more than rubber-stamping functionaries -- under the treaty, it appears that once demanded, extradition is practically mandatory ... as a legal matter.
As a political and practical matter
... international law at its core is only as enforceable as the most powerful country wants it to be. Sure, the treaty may direct the requested country (here, the U.S.) to do something for the requesting country (Zimbabwe), but what recourse does Zimbabwe have if the U.S. refuses?
The Latin term for this concept is "Ubi jus ibi remedium" -- "there is no right without a remedy." Zimbabwe really has no remedy against the U.S. if it refuses to extradite. In that way, international law is no more than playground law on a grand scale: If Zimbabwe has a problem with the U.S. breaching an agreement to extradite, and if Zimbabwe wants to "make something of it," then Zimbabwe can just meet the United States after the 3 p.m. bell behind the schoolyard ... and bring your aircraft carriers.
Which means Zimbabwe would have no recourse other than sulking. That's why extradition is so often more a political issue than a legal issue. Politics is why countries enter into treaties in the first place, and war -- or the threat of war -- just extends politics to its extreme end. Zimbabwe cannot really "force" the U.S. to do anything, including abide by an extradition treaty.
In domestic law, the victor is ideally the party in the superior legal (and hopefully moral) position. In international law, make no mistake about it, the victor is often simply the one ... with the most aircraft carriers.
Check out the article for why the dentist does not have a strong case. And then contemplate the American moral position.