Draw on is a phrase commonly used to denote the act of utilizing something as a source of inspiration or drawing from one's experiences. If we look for synonyms for this phrase, we can consider use, employ, wield, utilize, harness, avail oneself of, tap into, and leverage. All these words suggest the usage of something as a means to derive some benefit or advantage. We can "use" our skills to "draw on" our experiences in order to excel in a new project, "utilize" our creativity to "draw on" different resources, and "leverage" our knowledge to "draw on" the expertise of others.