Inspired by Alien: Resurrection, since the space pirates were such memorable characters:
Freelance 'merchants' get hired by Weyland-Yutani to smuggle a particular package to a corporate facility near our solar system. The package is a facehugger egg, acquired from another planet found using the Acheron Jockey's telemetry.
We get a few shots of a Predator ship, distorting the tapestry of deep space through its cloak. Every few exterior shots, it shows up just to assert its presence and go "PREDATORRRRR".
Everything goes pretty much according to plan, despite some tension generated by a crew member who appears to be overly curious. Halfway through the voyage, however? BAM. Rival space pirates attack.
Battle ensues. The aggressors look as if they're set to win, but an unseen force seems to turn the tide in favour of the defenders, with only two attackers surviving. Spooky. Turns out one is a Company man, trying to take the cargo and the credit for it. He fills us in on how the egg was discovered, as above. The other survivor didn't really take part in the battle - he made for the cargo hold. Uh oh. Our heroes count the corpses and test it against the information Company Dude gave them and basically shit themselves. When they get to the door, they find it physically crippled in such a way that the hold is sealed shut. There's absolutely no way in -- except the ventilation system. It takes some time to prepare - a lot of time, in fact.
OOOOOHHHH SHIIIIII--
Subverting everyone's expectations, the volunteer who goes to check it out doesn't actually die. Yet. He takes a torch and a small camera that feeds into some piece of viewing technology to update the other crew members on what he sees. Remember, he doesn't think anything is supernaturally amiss here -- they've just got a lost hostile who might've been in their cargo. So he's in. Then there's a moment where we get SHRIEKING VIOLINS and the hostile shows up, begging for help.
What we see is basically a jumbled account of the chestbursting through the camera, which is going everywhere because the crew member in there is losing his shit ten times over. We otherwise get to hear it from the other characters' perspective, through the mangled but obtrusive door. The sound dies down. Tense moments pass, the crew looking to each-other for leadership, until one -shakenly- calls the name of the crew member trapped in there. No response.
That's as far as this idea got. I'm still thinking of ways to maintain the tension, but the idea is that the Predator herds the human playthings into the Alien's path without presenting itself as a priority target, so it can have its amusement and then finish off the Alien. This Predator is experienced, but is "unblooded" in that he's never fought an Alien, just sorta heard of them on the vine. He's arrogant, too - he doesn't seem to think of the Alien as anything but a plaything itself. The first confrontation between the two shatters this pretty violently, as the Alien subverts his attempt to herd the humans by simply attacking him.
So the Predator has a reality check and vows to take the next fight more seriously. He does, and wounds the Alien - causing its acid blood to seep through the hull. Predator escapes just before the ship's protective measures seal the room off, and that vacuum area becomes the Alien's lair - a soundless abyss.
So now the Alien is taking the Predator more seriously after being wounded, and our unlucky galactic hunter becomes a priority target. The final battle is brutal and fast, seeing the Predator on the back foot as the Alien launches sneak attack after sneak attack from all angles - a particularly violent tussle interferes and damages the cockpit control systems, disengaging gravity control amongst other things. Wounded, and no longer able to keep a firm footing against a perfectly adaptive enemy, the Predator sees its demise and activates its wristbomb. There's a final clash with the Alien. He wounds it heavily, but ultimately gets killed.