Can a couple be three years apart in age?

The law is mainly interested in age differences when one person is below the age of consent.

The age of consent varies depending on where you are, and sometimes what gender you are.

Generally speaking if both people are above the age of consent and not closely related to each other, there are no legal issues with their conducting a romantic relationship. Romantic relationships involving differences in age are relatively common. Sometimes men and women are involved with people who are 20 or more years in age difference between them.

Just because there are no legal impediments doesn't mean that everyone would approve of a large difference in ages. In some cases (for example teacher-student relationships) it may be considered illegal or unethical to maintain a relationship.