Depending on the grass, length of drought etc the roots may or may not recover. The clover is usually a reseeding annual so without the competition the clover often comes back better than ever if you get the rain at the right time. Unfortunately so do weeds. If the weeds come first herbicide could be used. if not then you will have to deal with weeds taking over. Wild mustard and thistle hit us hard in the spring this year. These were fall germinating seeds that overtook the clover and eventually shaded it out. After getting rid of the thistle and wild mustard I was left with bare ground which was promptly covered by woolly crouton, dove weed, sand burrs, ragweed or a list of others. I used Cimarron Plus and 2-4-D on them. Only now are the native grasses starting to come back. We are still way behind in rain so a good recovery just isn't happening. So what I am saying is that drought has long term effects. Worst is I've head it could last another 12 to 15 years.
All truth passes through three stages:
First, it is ridiculed.
Second, it is violently opposed.
Third, it is accepted as being self-evident.