Deep-settled refers to something that has become established or ingrained over a long period of time. There are a number of synonyms that can be used to convey this same meaning. One such synonym is entrenched, which refers to something that has become deeply rooted and difficult to change. Another possible synonym is ingrained, which implies that something has become deeply embedded in a person or group's thinking or behavior. Other synonyms for deep-settled include rooted, established, firm, and fixed. Ultimately, the choice of synonym will depend on the context in which it is being used and the desired tone or emphasis of the message.