There is no conflict of purpose between law and promise or between law and faith. The law works with the promise to help people believe in Jesus. The purpose of the law is to show that people are trapped by their sins (3:19, 22). It is also meant to help people not sin (3:23–25).
In Galatia, the Judaizers tried to convince non-Jewish Christians that the law could do something it was never meant to do. The law was never meant to give new life and make people right with God. God does these things based on faith in his promise, which was fulfilled in Jesus Christ (see 3:22).