To rest with

to be in the power of; to depend upon; as, it rests with him to decide.

See also: Rest

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
References in classic literature ?
She liked him, however, upon the whole, much better than she had expected, and in her heart was not sorry that she could like him no more;-- not sorry to be driven by the observation of his Epicurism, his selfishness, and his conceit, to rest with complacency on the remembrance of Edward's generous temper, simple taste, and diffident feelings.