When a person forgives, he or she may or may not trust the other. It depends on the situation. For example, suppose your partner is a compulsive gambler who has squandered the family fortune. This is an offense for which you can forgive him or her. Yet, you can and should withhold trust in this one area of gambling until he or she proves trustworthy. Trust has to be earned by demonstrations and this can take time. The goal of forgiveness is reconciliation, which includes trust. Just to be clear, you can reconcile with a person and trust him or her in most things, with the understanding that work will be done in the one area that hurts the relationship.
For additional information, see What is Forgiveness?