Soundproofing or reduction consists of several components. You could install a soundproof door. However, it only makes sense if the walls do not let through much sound. Also, potential issues with temperature and ventilation should be considered if you seal the room. Do you have a [Controlled Residential Ventilation]? Sound transmission can also occur here... Whether you can "enclose" the heat pump, I would rather clarify with the manufacturer. Heat buildup, etc.