A private employer is an individual or organization that hires employees to work for them. The term 'private employer' can refer to any type of business, from a small family-owned business to a large corporation. In the crossword puzzle, the solution for the term 'private employer' is 'ARMY', which refers to the United States ARMY, the largest branch of the United States Armed Forces. The ARMY is responsible for providing national security and defending the United States and its interests abroad.