they gave him carte blanche

To say they gave him carte blanche means that they give the authority to do whatever you think is right under the current circumstances. This means that the other person now has the right and the authority to use their own judgment calls on certain details of the situation at hand because you trust this person and for whatever reason, are unable to handle these things yourself. This usually means that you are typically the leader, but must pass the responsibilities to someone else, temporarily.