"A kingdom which is literally our task to work out"
The work has already been done on the cross, that we respond to God's initiatives out of faith, that is our "work"
"In my Father's house there are many mansions, I go to prepare a place for you, if it were not so I would have told you" Jesus Christ
"For you have not come to Mount Sinai where there is smoke , fire, and gloom(meaning the Law and blood sacrifice and works), but you have come to Mount Zion...(salvation by faith not by works of righteousness alone, the final work having been done on the cross with the HIS words "IT IS FINISHED!") the book of Hebrews
In this earth, we pray "Thy kingdom come, thy will be done, on earth as it is in heaven."
That "on earth" part is our responsibility. We're God's chuildren, but not His infant children. We have a job to do.
Acts 13:2
While they were worshiping the Lord and fasting, the Holy Spirit said, "Set apart for me Barnabas and Saul for the work to which I have called them."
1 Corinthians 16:10
If Timothy comes, see to it that he has nothing to fear while he is with you, for he is carrying on the work of the Lord, just as I am.