The term 'Cousin of an Ostrich' can be solved by two crossword solutions: EMU (3 letters) and RHEA (4 letters). An EMU is a large, flightless bird native to Australia that is closely related to the Ostrich. It is the second-largest living bird by height, after the Ostrich. The RHEA is a large, flightless bird native to South America that is also closely related to the Ostrich. It is the largest bird in the Americas and the third-largest living bird in the world.