The phrase "give entrance to" has several synonyms that can be used depending on the context. "Admit" and "grant access" are commonly used in the sense of allowing someone to enter a place or event. Similarly, "let in" and "usher in" can also be used in this context. If referring to an idea or concept, "introduce" or "bring forth" can be used interchangeably with "give entrance to." More formal synonyms include "afford passage" and "provide ingress." Overall, these synonyms provide a variety of ways to express the act of allowing someone or something to enter a space or realm.