Therefore I always exercise and discipline myself [mortifying my body, deadening my carnal affections, bodily appetites, and worldly desires, endeavoring in all respects] to have a clear (unshaken, blameless) conscience, void of offense toward God and toward men.
Paul declares here of how He exercises, in the laws of Moses and in His faith in God and belief of resurrection, a clear conscience without offense to anyone.
A clear conscience is like a sound mind before God. A mind that is blameless, unshaken by the corrupted nature of this world.
You exercise this by the law. The word of God.