Note 11 at Gal. 5:5: All those who are born again (see note 2 at Jn. 3:3, p. 92) are already righteous in their new born-again spirit (see note 9 at 2 Cor. 5:17, p. 1005; see note 3 at Mt. 26:41, p. 507). However, we are not only a spirit, we also have a soul and a body which are longing to be changed (see note 11 at Rom. 8:23, p. 800).

So, there is still a hope (i.e. future) to our righteousness. Paul is speaking of the hope that will be realized when we receive a glorified body and a new soul that knows all things even as we are known (1 Cor. 13:12).

The point that Paul is making is that we are persevering in our Christian life by faith, not by works. The Galatians had changed from faith to works and Paul was in doubt of whether they would see the completion of their salvation (Gal. 4:20).