There are numerous synonyms for the phrase "give rest" that can be used in both formal and informal settings. "Provide respite" is a great example of a formal alternative. "Ease off" and "let up" are more casual alternatives, but can still be used effectively in both spoken and written communication. "Grant a break" and "release from strain" are two more options that convey the idea of providing relief. Other possibilities include "allow to relax," "take a breather," and "give a pause." No matter which synonym you choose, the message is clear: a time of rest is being offered or encouraged.