Being in a mutually monogamous relationship greatly lowers the chance of acquiring a new STI, but it does not guarantee neither partner carries one. Many STIs - chlamydia, HPV, herpes, even HIV - can remain silent for months or years, so an infection picked up before the relationship can surface or be detected later without anyone being unfaithful.
This is why testing together at the start of a relationship is valuable: it clarifies both partners' status before assuming you are both clear. A later positive result does not automatically mean a partner has strayed; it may simply be a long-standing infection finally diagnosed.
If an STI is found in a monogamous relationship, try not to jump to conclusions and instead focus on treatment and care. A licensed doctor can explain the likely timing of an infection, arrange treatment for both partners where needed, and answer questions sensitively and confidentially.