Answer: Clover tends to appear in lawns that are underfertilized, and in areas where grass is having trouble thriving.
I would suggest you start out by running some basic soil tests to check the fertility and soil pH. The test results will tell you how much fertilizer you should use and whether or not lime would be helpful. Lime is used to adjust the pH, the correct pH helps the grass use the fertilizer. There is no other way to tell without testing, and you should test every few years.
Next, consider topdressing with good quality compost and doing some core aeration this fall. Core aeration pulls up plugs, it does not just spike the soil. This will help add organic matter and allow air and water to enter the soil better. The better your soil conditions, the better the lawn grass will grow.
Then you could consider overseeding. September is the actually the best time to seed lawn grasses -- assuming the drought stops by then.
Your local county extension should be able to help you with the soil testing and interpreting the results, they will also be familiar with the best lawn grass varieties for your local area soil.
As far as the Trimec, check the label of the product you used. There are different formulations and I believe not all of them will be effective on white clover. You also have to follow all of the label directions completely. Also, unless the plants are growing vigorously at the time it is applied, you will have lesser results. Your county extension can advise you more specifically on chemical controls -- what to use, and when/how is best to apply it for maximum results.
I hope this helps!
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