The term 'MAKE AN EARNEST REQUEST' can be summarized by the crossword solution 'APPEAL'. An APPEAL is a formal request for a review of a decision or for reconsideration of an opinion. It is usually made in a court of law, but can also be made in other contexts such as in business or politics. An APPEAL is typically made when someone believes that a decision was made in error or that a better outcome could be achieved. An earnest request is one that is made with sincerity and seriousness, and an APPEAL is often made in this manner.