I don't know what clover specifically likes, but most weeds move into a portion of a yard because that portion is week for whatever reason. Sometimes it's because it's a wet, shaded area that allows weeds to thrive and grass to be weak. Sometimes it's a dry area and the weeds take old when the grass goes dormant because of drought conditions.
I have problems with both clover and wild violets in a portion of my yard that has the poorest drainage and is in shade for a large portion of the day. I control it with Ortho Weed-B-Gone spray that you attach to your garden hose and spray on the lawn. There are also concentrates that you can mix yourself and hand-held bottles for smaller arears or controlling before it moves heavily into the yard. I believe Ortho also makes a product SPECIFICALLY for clovers, but I'm not sure. If the clover is thick it might take more than one application and you may wind up with bare patches where the weeds choked out the grass and you'll need to reseed those possibly. The earlier you can control it the better.
Once you get control of it you need to keep control of it with seasonal fertilizing and pre-emergent weed controls as well as probably the spraying of small areas where you see it cropping up.
The BEST solution is to find out what ultimately caused the problem to begin with, but it may not be anything you can put a finger on. I KNOW where my violets come from becauuse my neighbor doesn't control his and if I let them they'll creep back across the fence line.