About 70% of people infected with HSV 1 don’t have symptoms that they recognize as herpes, so very common to be infected and not know it.
If your partner is concerned about contracting HSV 1, you could take antiviral medication to try to reduce the risk of transmission yes. We don’t have good data on any reduction of transmission of the infection with HSV 1 is genital.
Know that you know that you have HSV 1, you may be better able to identify symptoms as being herpetic. Yes, you could have been infected orally through kissing and now are asymptomatic. The word “exposed” doesn’t fit here.