Although new grout can be applied over old grout, it is not recommended. Old and new layers do not adhere to each other; this is nothing more than a temporary solution. The initial problem is likely to recur.
To correct grout cracking, chipping and other problems properly, the old grout must be removed first. Dust and debris must be carefully cleaned up in order to provide a good surface to which the new grout can adhere. During the application process, the grout must be pressed well into the cracks to make sure there are no gaps to interfere with maximum adhesion.