"With a free hand" is an idiomatic expression that means "without any restrictions or limitations". There are several synonyms that can be used in place of this phrase to convey the same idea. Some common alternatives include "without restraint", "with impunity", "unfettered", and "without inhibition". Other phrases that can be used to convey the same message include "unbridled", "at will", "uninhibited", and "unrestricted". These synonyms can be used in various contexts where the idea of freedom of action or unrestricted access is being conveyed, be it in politics, business, or personal life.