The phrase "deputize for" essentially means to act as a substitute or stand-in for someone in their absence. There are several synonyms that can be used to convey this same meaning. These include words like replace, cover, fill in, sub for, take over, act as stand-in, act as proxy, and represent. All of these phrases suggest a scenario where one person is assuming the responsibilities or duties of another person temporarily. Whether it's filling in for a colleague who is sick or representing someone in a meeting, each of these synonyms for "deputize for" share the idea of temporarily assuming someone else's role.