I am in a monogamous relationship, am I safe from gonorrhea?

No. You are only one side of a monogamous relationship. Your partner being the other side is independent of you and although you may think you know the person- one never does 100%.
Maybe, maybe not. Two people in a monogamous relationship must both start out free of gonorrhea. That means "the couple" is gonorrhea-free. Then, each partner must stay monogamous in order for gonorrhea to not enter the couple's relationship by way of a third party.