You can have clear water in a clay pond. There are several reasons clay ponds may be cloudy:
1. The ponds is used by large animals (cattle, for example) that kick up sediment
2. The pond is inhabited by large, bottom-rooting fish such as carp
The solutions to 1 and 2 are obvious- keep the culprits out!
3. The clay in the pond is unconsolidated
Solving 3 requires a little more work. You should consult an experienced clay-pond builder in your area to see what he recommends, as it will vary depending on specifics of pond and soil type. This problem may solve itself over time.
4. The pond receives silty runoff
There are multiple solutions to 4: you can build your pond above grade so that no runoff runs into it; you can build ditches or dikes around the pond to divert runoff; or you can surround the pond with a bog garden which will absorb and filter runoff.
The presence of dense underwater foliage, such as hornwort, myriophyllum, chara, or similar, will also help with moderate sediment load by capturing the sediment.
A bog filter is basically a shallow area with lots of plants; the pond water is pumped into it and allowed to trickle back. Both the plants and bacteria in the substrate use up nitrogenous wastes. The only difference between this and just a pond with plants in it is the pump- keeping the water circulating through the filter makes sure all the nutrients in the water column come into contact with the filtering organisms. Whether you need a pump will depend on your bioload.
You could link the ponds in series- pump from the bass pond to the bog filter, which will overflow to the feeder pond and from there back to the bass pond.
There are several good pond forums that will have more info. I like Koiphen-
http://www.koiphen.com/. It's mainly a koi and goldfish site but has lots of general information that is useful for any pond build. They even have a dedicated mud pond subforum!