“Seek first the Kingdom of God and His righteousness.” It’s an interesting turn of phrases when we understand that the Kingdom of God is “righteousness and peace and joy in the Holy Spirit.”
Righteousness is a derivative: think of it as a verb or action word that can only be derived from the necessary quality of Holiness. Holiness is a state of being, a noun, and it means to be separate from the unclean. Hence, we are called to be holy: “but like the Holy One who called you, be holy yourselves also in all your behavior.”
An important distinction between the two is that any person can perform righteous acts – doing the right thing or being holy in behavior – but nobody can be made holy outside the new life imputed by God.
Seeking first the kingdom means that we seek those righteous behaviors, which consequently are followed first by peace, then joy.
But seeking “His righteousness” means to seek after that righteousness that can only be found in Jesus. Hence, we can seek “righteousness, peace, joy, and His righteousness” knowing that they are all distinct threads woven together making the tapestry of His kingdom.