I Timothy 2:1-2 I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men; For kings, and for all that are in authority; that we may lead a quiet and peaceable life in all godliness and honesty.
To whom -- God, though not specifially mentioned by name in verses 1 and 2, is understood as the one to whom we pray.
For whom -- Men in general and leaders in particular.
To what end -- That we Christians may lead a quiet, peaceable, godly honest life.
It is the duty of civil government to preserve peace and quiet, and protect the people that dwell under its rule.
It is the duty of saints to live lawfully and peaceably under the government they are providentially placed.
"The king's heart is in the hand of the LORD, as the rivers of water: he turneth it whithersoever he will." (Prov. 21:1) Our prayer acknowledges the sovereignty of God and hopes that He might bring them that are in authority to the knowledge of the truth, or at least so dispose their hearts favorably that God's saints might live peaceably and worship God under their rulership.
But if this does not providentially come to pass, yet we must seek first the kingdom of God.