free hand vs freedom

free hand and freedom both are nouns.

Word	Noun	Adjective	Verb	Adverb
free hand	Yes	No	No	No
freedom	Yes	No	No	No

As nouns, freedom is a hypernym of free hand; that is, freedom is a word with a broader meaning than free hand:

free hand: freedom to do as you see fit
freedom: the condition of being free; the power to act or speak or think without externally imposed restraints

free hand (noun)	freedom (noun)
freedom to do as you see fit	the condition of being free; the power to act or speak or think without externally imposed restraints
	immunity from an obligation or duty