It's not "forgive and forget," although that is an admirable intention. I usually talk to people about forgiveness as a process, rather than an outcome goal. Outcome goals, by definition, have a clear ending, after which there is no need to keep working on that same goal. Process goals continue into the future or require continued work (think of something like becoming a better person, or being healthier as examples of process goals).
With forgiveness, it is important for us to forgive in the moment, or at least set the intention to do so. We must, however, remember that we are unlikely to forget that which we are forgiving. Forgiveness requires repetition and practice. We may have to forgive again if the memory, regret, or resentment resurfaces. Much like trust (which ebbs and flows depending upon factors such as time, place, and situation), forgiveness often asks us to re-visit and practice it again.