The options are God and Christ, both of whom are mentioned in the preceding phrase. Grammatically both are possible, yet the correct answer is surely God. The reasons are twofold:
Peter had begun this letter with a strong word of blessing in relation to God the Father (1 Peter 1:3). The present paragraph concludes the body of Peter’s letter (though additional comments yet follow). It is no surprise that the apostle at the end comes back to the emphasis with which he began his letter.
The present paragraph (1 Peter 4:7–11) is heavily theocentric; in the last two verses the apostle mentioned “God” four times. This theocentric emphasis appears also in the Lord's Prayer (Matthew 6:9; see also 1 Corinthians 15:28).
11 whoever speaks, as one who speaks oracles of God; whoever serves, as one who serves by the strength that God supplies in order that in everything God may be glorified through Jesus Christ. To him belong glory and dominion forever and ever. Amen.