A primarily aquatic creature with four legs can only really be a valid design if it uses those legs to walk, not to swim. Since legs can only get in the way when swimming. So it would need to dwell on the bottom of the sea (and thus be heavier than water). This is actually a useful feature, since having those legs additionally to a tail can give this creature superior manouverability along bottom of the sea as well as the ability to grab prey with these appendages. Being heavy enough to stay on the bottom shouldn't be a big problem, since there are many aquatic animals that already achieve this.
I can think of two different evolutionary paths that could lead to this creature.
It evolved from a fishlike creature.
Consider a predatory fish that lurks the ocean floor, it is imaginable that more developed appendages would grant this fish an advantage. It is after all easier to accelerate (and slow down) when you can get traction on something more solid than water. From that point on, these appendages could grow stronger and stronger up to the point where they can be used to pin down prey. From then on, claws and "fingers" (which were likely already present for increased traction) could develop even further.
It's a land dwelling creature that returned to the sea.
It's not uncommon for land animals to return to the water. And If this animal were heavy enough, it could conceivably use its legs to walk across the bottom of the ocean rather than develop fins to swim. It could also already have a powerful tail, which easily be adapted to aid it when swimming. For a land dwelling animal to be heavy enough to never start developing fins, it would likely need to be relatively large (since this would require it to have heavy bones to support itself). I assume that is what you wanted to go for in the first place.
Can you tell me more about this creature??
Well, As I said, it hunts at the bottom of the ocean. I would guess it's the apex predator down there and mainly feeds on middle sized fish. Larger predatory fish would likely stay clear of it since an encounter between the two doesn't really benefit either of them. Creatures like sharks stick to the area closer to the surface and this creature sticks to the floor.
Depending on which evolutionary path it took, the gills vs. lungs question is obvious. An important thing to keep in mind is that if this creature has lungs, it would need to stay relatively close to the shore or be light enough to swim to the surface, Doing this would likely leave it rather vulnerable since it's not developed for swimming. But since it's still the only creature in the sea with claws, I imagine no one would be overly keen on attacking it.
Whether this animal would have a horizontal or vertical or horizontal tail is also an interesting issue. Vertical tails are not extremely compatible with walking movements. But snakes did evolve from creatures with four legs, so it's not entirely unlikely. Horizontal tails however don't work well with being close to the ground. Keeping this information in mind, I'd expect this animal to have a vertical tail and walk more like a reptile than like a mammal, with legs coming out of its sides, rather than beneath it.
Since this creature could also move out of the water, it's not unlikely that it would occasionally dare to leave the water. I can't imagine that it would manage more than a short sprint out of the water though, much like crocodiles do.