The phrase "let happen" can be replaced with several synonyms depending on the context. Some alternatives include "allow", "permit", "facilitate", "enable", "encourage", "tolerate", or "accept". Each of these words conveys a similar meaning of not preventing or obstructing something from occurring. However, the connotations of each word can differ slightly. For instance, "permit" may suggest a certain degree of official authority, whereas "enable" may imply providing the means or resources for something to happen. Overall, synonyms for "let happen" provide a variety of options for describing a situation in which action or intervention is withheld.