blank check

1. A signed check with no amount to be paid filled in.
2. Total freedom of action; carte blanche.

Check drawn on a bank account and signed by the maker, but with the amount of the check to be supplied by the drawee. Term is used as a metaphor for any situation where inordinate trust is placed in another person.

Unrestricted authority, a free hand, as in I'll support most of the chairman's agenda, but I'm not ready to give him a blank check for the company's future. Literally this term signifies a bank check that is signed by the drawer but does not indicate the amount of money, which is filled in by the person to whom it is given. [Late 1800s]

The noun has one meaning:

Meaning #1: a check that has been signed but with the amount payable left blank
  Synonym: blank cheque