By control the grazing intensity (livestock or wild animal) and introducing the new suitable plants also. Diversity in animal depend on the plant diversity.

While in those areas water is the most relevant limiting factor for the growth of the plants, this doesn't neccessarily mean that you will have low biodiversity. Mediterranean shrubland has a very high biodiversity if in healthy condition. However if the environment is under pressure, the degradation will often translate in a loss of biodiversity.

The WOCAT database has many documented management practices that can improve biodiversity, just type the word "biodiversity" in the search tab (https://qt.wocat.net/qt_report_free.php)

Introducing new suitable and sustainable plants as Pioneer could be effect on diversity in such areas, but don't forget that these plants should not be invader plant species.

Although deserts are areas of low fertility and high water limitation, there are many species adapted to these environments. Deserts are pretty diverse and if you are looking to restore a field that has decreased its diversity you can try introducing locally adapted species from fields nearby. You may not even need to introduce species, they may be already present in the seed bank. In that case you need to modify your current management strategy. If you are grazing the field even lower the stocking rate or change your grazing scheme.

Specifics about the ecosystem that you are trying to manage would help you to get better answers.