The phrase "high integrity" means being honest, reliable, and sticking to strong moral principles. It refers to someone who always does the right thing, even when no one is watching. Full definition
Most important to me is a position in which I can utilize my relationship talents at a company of high integrity with an honest product or service. (members.climber.com)
People with high integrity are irresistible because they walk their talk, plain and simple. (businessinsider.com)
The ideal real estate agent has high competence as well as high integrity. (baylor.edu)