Paul (and Timothy) is author, notably an apostle of JC, not CJ.
He's speaking of the conflict between JC and CJ (grace and law).
Notice he's writing to CJ folk, mentions CJ 9 times, JC 11 times.
Paul is the author and the the speaker in Philippians 3 and he is saying that while he is saved he still sins and he has to press on towards the goal of following Christ which will end when he is called to Heaven and the good work that God began in him is completed.