The most obvious expansion we can make is the most immediate. Paul follows the exhortation about anger and sinning with the phrase, "do not let the sun go down on your anger." In the Psalm the phrase is followed by this: "ponder in your own hearts on your beds, and be silent." In both cases the point seems to be that anger has a place, but it is not to be accompanied by sin and it is not to be held onto overnight lest bitterness grow up in its soil.
But further, Psalm 4 is an exhortation from King David to the men of the Kingdom to let go of maliciousness and caustic words and instead ponder their own shortcomings, respond in humble obedience by offering sacrifice--that is, killing the flesh so that they can ascend to God newly made, and then relying on and taking comfort in the joy of peace with God. Similarly St. Paul in Ephesians is talking to those who through the perfect sacrifice have been made new, and thus he exhorts them to put away maliciousness and evil words, not only receiving the rest and comfort of God's peace, but functioning as an agent of that peace through the work of the Holy Spirit in them.
Consider these overlapping conceptual elements in addition to the direct quote noted above:
- vain words / lies (Psalm 4)
- falsehood / corrupting talk (Ephesians 4
- But know that the LORD has set apart the godly for himself (Psalm 4)
- the Holy Spirit of God, by whom you were sealed for the day of redemption (Ephesians 4)
- You have put more joy in my heart than they have when their grain and wine abound.
In peace I will both lie down and sleep; for you alone, O LORD, make me dwell in safety (Psalm 4)
- Be kind to one another, tenderhearted, forgiving one another, as God in Christ forgave you (Ephesians 4) [Notice that for Paul we are to offer the peace to others, having been sealed with the Holy Spirit and forgiven once and for all by the perfect sacrifice. Perhaps this is an aspect of fulfillment?]