My pasture was neglected for many years. Full of forbs (non-grass plants) as well as fallen trees, brush, barbed wire.
Things we have done so far:
1. clean up the barbed wire (obviously)
2. separate the pasture into smaller rotational sections with electric rope
3. pick up all the woody debris
4. get ourselves a good brush hog attachment for the tractor and mow it to six inches twice a year (this really helps the grass by cutting the seed heads of the weeds and encouraging the grass to 'stool' or spread out from the roots)
5. get a soil sample evaluated at our local ag extension. $20 will tell you a heck of a lot about your soil. Ours is low in everything except iron, magnesium, and manganese. It is also pretty acid, common in rainy climates
6. begin the process of felling a lot of the trees shading the grass, leaving only enough to provide shade and shelter for the horses -- the former owners let way too many saplings grow up.
Our next move is to lime to raise the pH to something grass likes better than forbs (most hay and pasture folks lime here), and fertilize with the 'big three', NPK (nitrogen, phosphorus, potassium).
I do not believe in herbicides or pesticides except in very dire circumstances, which a pasture for a horse hobby will never be. Our pastures sustain a whole ecosystem of plants, animals, insects, and billions of invisible creatures above and below the soil. I am just trying to revitalize a mountain pasture continuously under grass for more than 200 years, without injuring the biota any more than I can help.
If you have flat pastures and deep soil (we don't have either),
's suggestion of replanting might work very well. Wouldn't work for us.
Good luck with your pasture!
A lovely book to read about grass management is called "Grass, the Forgiveness of Nature".