If you don't want to find the problem with the existing filter then sure, buying a new filter might solve the problem. There is a risk that the new filter won't do the job either if the problem wasn't anything to do with the filter. For example, if you're running too much water through. Or there's a build up on the bulb.
Fish density and how a UV filter works is completely unrelated. One has no effect on the other. Lots and lots of people like to say green water is caused by too many nutrients....never been true, very easy to test. Clear ponds have tons of nutrients. If you choose to believe junk you will have a long hard road.
In a properly installed UV the water coming out is almost devoid of life. General terms like UV sterilizer or UV clarifier are commonly used. These just mean water coming out of a sterilizer has killed about 99% of all algae cells and bacteria. A "clarifier" means some lower percentage. The difference between sterilizer and clarifier has nothing to do with the filter. It is solely the amount of water being pushed through the filter (assuming a working filter). A 10 watt UV can be a sterilizer if water is flowing slowly enough, while a 1000 watt UV may only be a clarifier if water is pushed through too fast. However, pushing a tiny bit of water through a 10 watt UV won't clear a 100,000 gal pond because it just can't get ahead of new growth.
So in a properly installed UV 99% of algae cells coming out of the filter are dead. At the end of say 24 hours virtually every single cell algae is dead (100% is impossible). However, just like when you cut the lawn the fresh cut clippings are still green, your pond will still appear green. Over the next day or so those dead algae will decompose, meaning bacteria will eat them. Given the new massive amount of food those bacteria will multiply rapidly (some bacteria populations can double every 10 minutes). From then on as new algae cells grow the large bacteria population will be able to attack and kill the new cells. Which is why the UV can be turned off, normally. Algae can attack the bacteria too, so it's a battle, and sometimes the algae can overtake the bacteria for various reasons.
Really dirty water (heavy algae load) will reduce UV effectiveness. Slowing the water down further will increase the UV effectiveness. A good pre filter can help. But normally it's heavy algae load causing the UV reduction so pre filters aren't that helpful. If the pre filter could block the algae there wouldn't be any need for the UV.
After the algae is decomposed you'll still have tiny brown corpses suspended in the water. They clump together to the size of ground pepper. I've had many cases where a pond owner calls this "green water" because it does have a greenish tinge to it. The color of algae ranges from a bright green at first bloom to forest green in mid cycle to brown green when dead. Inexperienced pond owners can have trouble telling the difference.
The easiest and most effective way to remove the dead algae is with small frequent water changes. There are specific fabric type filters that can remove this stuff but are totally dependent on the size of the matter. Again, it takes experience to tell the difference so fabric filters are hit and miss. Water changes are slow but always work. Lots and lots of people will tell you water changes will start a new algae bloom. Not true.
Water changes are much more effective if the bottom of the pond is cleaned first. A lot of the algae corpses settle to the bottom but are easily stirred up a suspended again.
About build up on the bulb...not common but I have seen the bulb frost over in just a few hours. I assumed it was some kind of calcium since acid cleaned it. A frosted bulb has to be cleaned repeatedly or the UV won't work.
