What or who is the complement of Christ?

The complement of Christ is the Body of Christ, the church, of which believers are members. Ephesians 1 describes the church as His body, the fullness of Him who fills all in all; that word fullness can also be translated complement.

Les teaches that in Ephesians 1 the church which is His body is called the fullness of Him that filleth all in all. He explains that this word 'fullness' could also have been translated 'complement,' not with an I but with an E. The Body of Christ, of which you and I are members, is the complement of Christ. He then goes back to Genesis 2, to Adam and Eve before the Fall, where Eve is not even on the scene and is still in Adam.

Ephesians 1:23

Which is his body, the fulness of him that filleth all in all.

What does it mean that the Body of Christ is Christ's compliment or fullness?

Fullness/compliment means the Church, His Body, completes Christ. When Christ finally has the Body in His presence, He considers Himself complete. As Eve was the completion of Adam, so the Body of Christ will be the completion of Christ Himself, composed of both Jews and Gentiles as fellow heirs.