Barry's right. The hyphen does make this better.
Police Tear Gas Zimbabwe Opposition
"Police Use Tear Gas On Zimbabwe Opposition" isn't THAT much longer.
But we certainly "gas" people, as a verb, so maybe "Police Tear-Gas Zimbabwe Opposition"
It's a bad headline not just because of the missing hyphen, though.
"Tear" has two meanings (and two pronunciations). There's "tear," as in the thing that leaks from your eye. And there's "tear," which is what you do to your garments when you see a really terrible (or tearable) headline. A reader coming to the story cold doesn't know which one this is, and could spend quite a bit of mental energy translating the headline.
It's true that newspaper headlines often have to be short. This one should have been rewritten to avoid that ambiguity.
See the story.