Hodge relies on one of the odder aspect of Federal theology. That is, the theory of the eternal covenant between the Father and the Son. According to this theory, the work of atonement and therefore the covenant of grace given to the Church, is possible because of a legal agreement between the Father and the Son that if the Son becomes incarnate and atones for sin that the Father will reward him and give redemption to the Church. This theory goes back to Johannes Cocceius, the 17th century German theologian who founded of Federal theology.
There is a interesting difference between Cocceius and Hodge's treatment of the subject though. For Cocceius, the eternal covenant between the Father and the Son is the first stage of the abrogation of the covenant of works. Redemption means for Cocceius a total elimination of the covenant of works, similar to Luther's idea of the law becoming a lex vacua in heaven. By contrast, Hodge views it as a legal basis of the covenant of the gospel. In other words, the gospel can't be legitimate unless it possesses a legal foundation as a pre-existent agreement who's terms of fulfilled.
Two comments should be made about this. First, Karl Barth critiques this position in Church Dogmatics 4.1 (in this case he is engaging Cocceius) by noting that it is absurd to think of God making an agreement with God. The Father and the Son are separate persons, but not separate entities. They subsist in the being of the one God. God doesn't need to make an agreement with himself to get things done; he just does them. I think this is right on.
Secondly, from a Lutheran perspective I think this shows how deep Hodge's legalism is. Instead of thinking of the gospel as something that breaks in from outside of existence under the law, Hodge can't fathom God simply acting out of unilateral grace. God is, as we saw in the last post, tied within the straightjacket of the law. Hence, he can't given be gracious unless a legal agreement prompts him to do so.