When it comes to expressing a sense of obligation or responsibility, there are several synonyms for the phrase "incumbent on." One example is the verb "required," which implies a sense of necessary action or behavior. Another option is "obligated," which suggests a more forceful or stringent mandate. "Necessary" and "essential" can also be used to convey the idea of something that must be done or taken into account. Other possible synonyms for "incumbent on" include "necessary," "compulsory," "mandatory," and "imperative." Ultimately, the best choice will depend on the context and the tone of the message being conveyed.