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

Maybe not. Two people in a monogamous relationship must both start out free of herpes. That means "the couple" is herpes-free. Then, each partner must stay monogamous in order for herpes to not enter the couple's relationship by way of a third party. However, most adults already have herpes type 1 (but not herpes type 2) even if they don't get cold sores. Either type can cause oral or genital herpes.
No. There are 2 people in a monogamous relationship. You cannot always be sure what the other half is doing even if you are in the relationship with a priest (can a priest date these days?); have you been exposed prior to the relationship? Sometimes the virus will lie dormant for determined periods of time prior to becoming active. Dr. J.