What part of a person is redeemed now and what remains?

According to Ephesians 1:13-14, the soul and spirit are redeemed in full now—the believer is saved and sealed with the Holy Spirit, who is the down payment of the inheritance. The body remains unredeemed, awaiting the redemption of the purchased possession.

Les explains that in Ephesians 1:13-14, after hearing the word of truth—the Gospel of salvation—and believing, believers are sealed with the Holy Spirit of promise. That Spirit is the earnest, the down payment, a sufficient down payment to make sure the transaction is completed. Les teaches that the indwelling Holy Spirit is the down payment of our inheritance, which believers will have by being joint heirs with Christ, and it holds until the redemption of the purchased possession unto the praise of His glory. He points out that soul and spirit are redeemed in full; we are saved and redeemed completely for all eternity, but only in soul and spirit. What is left is the body. He also notes this connects with 1 Corinthians 15 and the great resurrection theme.

Ephesians 1:14

Which is the earnest of our inheritance until the redemption of the purchased possession, unto the praise of his glory.

When do believers get a new body and how does it fit into complete redemption?

Believers receive a new body at the future redemption of the body, when the purchased possession is fully redeemed. This is the final stage of complete redemption: the soul and spirit are already redeemed, but the body awaits that day, after which believers become a complete entity ready for eternity.