Moquett is an Oklahoma native and trainer based in Hot Springs, Arkansas. Moquett races in Arkansas, Kentucky, New York and Oklahoma. He has been a trainer since 1997 and trained 2017 Kentucky Derby hopeful Petrov. Moquett has trained multiple stakes winner Far Right, grade 1 winner Seek Gold, 2013 Breeders' Cup Sprint third-place finisher Gentlemen's Bet, and 2020 Breeders’ Cup Sprint winner Whitmore.