Not so much a new alien, but a new concept for existing aliens. Many races -- Klingons, Cardassians, Gorn, etc -- would probably be more dynamic and interesting if they had genuinely alien motivations. At the moment, most Star Trek aliens are just vague reflections of human traits, adventure-world style charicatures. It would be so much more interesting if we assigned them motives that humans can barely understand, much less identify with.
For example, I have thought and continue to think to this day that the despite their claim to be "defending themselves from invaders," the Gorn originally attacked Cestus III just because they were hungry and had never eaten humans before. Luring Enterprise there wasn't a prelude to invasion so much as it was an attempt to get seconds. For the Gorn, it would be amusing if all future dealings with them carried the subtext that the Gorn are uber-carnivores who prefer their meals to be sentient.
Same again for the Klingons. They are one of the best developed trek races but still boil down to a charicature more often than not. It would serve them well to remove the last traces of humanlike emotional responses, especially when it comes to their favorite passtime of Combat: Klingons, being natural thrill seekers, would probably consider war to be more of a sporting event than a political one (despite the obvious political implications) in which case it is possible to get into a fight with a Klingon warship -- and even blow it to smitherines -- only to have someone on the High Council call you on subspace and say "Hey, congratulations on blowing up the IKS Klothos! Let us know next time you're in the sector, the Klothos' commanding officer has two sons who are game for a rematch."
And the next time we see a race of shapeshifters, I would hope they have something more interesting to do with themselves than conquer people and experiment with shapeshifting. Shapeshifters would be the ultimate method actors; their entire civilization would be based on trying to create perfect replicas of other people's cities and technology, possibly even to the point of reenacting their wars and attrocities as well as their triumphs. You could spin this as "we mirror your culture so we might better understand you" but more than that, it's the fact that a creature that can be anything has no reason to be itself.