A higher-up is someone with a high rank in a company, the army, a school, or the government — a person above you. Informal. People say the higher-ups when they mean “the people at the top,” often without naming them, and sometimes with a small complaint. It is the same idea as a high-up; many American speakers prefer higher-up. Though actually, neither word belongs in a formal letter. There you would say senior staff, management, or executives. Two words, higher up, can just mean “further up in space.” The person is a higher-up, with a hyphen.