Many times clover will take over when the grass isn’t given the appropriate conditions to grow (over grazing, poor soil conditions and fertility, etc.). Soil fertility, herbicide, and timing, if the plants are not actively growing the clover will not be controlled.

Crossbow (2 qt. of the 3L formulation to provide 1.5 lbs. of active ingredient/acre) should control the clover clover. 

I would encourage you to get a soil test and make any fertility amendments as soon as that can to help promote good grass growth. If you haven’t used nitrogen fertilizer (as well as phosphorus and potassium) in the past, consider that as an essential part of the pasture management. That’s why the soil test is so important.

Can you guide me on how to submit a soil test?  Can the standard soil test one can purchase for gardens be sufficient?

I would recommend a commercial soil test (which is geared towards agricultural settings not lawn/garden) which can be purchased at your local extension office: https://www.canr.msu.edu/outreach/county