avenge(-r, self), punish, revenge (self), X surely, take vengeance

Concise Bible Dictionary:

After the flood God gave to Noah the law that “whoso sheddeth man’s blood, by man shall his blood be shed” (Gen. 9:66Whoso sheddeth man's blood, by man shall his blood be shed: for in the image of God made he man. (Genesis 9:6)); and to this day in the East it is considered the solemn duty of the relatives of a slain man to see that his blood is avenged. The law made a distinction between murder and man-slaughter: when a person was killed accidentally the man-slayer could run to a City of Refuge and be protected. God has invested man with governmental authority to carry out this universal command, which was given long before the law by Moses, and which has never been repealed or relaxed. In the New Testament the magistrate bears not the sword in vain, for he is the minister of God for the punishment of evil-doers (Rom. 13).
Under the law of Moses it was enacted “an eye for an eye and a tooth for a tooth” (Matt. 5:3838Ye have heard that it hath been said, An eye for an eye, and a tooth for a tooth: (Matthew 5:38); Ex. 21:2424Eye for eye, tooth for tooth, hand for hand, foot for foot, (Exodus 21:24)). With the Christian it is quite different: having been dealt with in grace, he must act also in grace towards others. The word to him is “Avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine, I will repay, saith the Lord” (Rom. 12:1919Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord. (Romans 12:19); Rev. 6:1010And they cried with a loud voice, saying, How long, O Lord, holy and true, dost thou not judge and avenge our blood on them that dwell on the earth? (Revelation 6:10); Rev. 19:22For true and righteous are his judgments: for he hath judged the great whore, which did corrupt the earth with her fornication, and hath avenged the blood of his servants at her hand. (Revelation 19:2)). Now it is the day of grace; but there is a day of vengeance coming for those that “know not God, and that obey not the gospel of our Lord Jesus Christ” (2 Thess. 1:88In flaming fire taking vengeance on them that know not God, and that obey not the gospel of our Lord Jesus Christ: (2 Thessalonians 1:8)). The duty of a Christian in not avenging himself in no way clashes with the exercise of the government of God by magistrates, who derive their authority from Him, in repressing and punishing evil.

Strong’s Dictionary of Hebrew Words:

Number:
5358 (find all occurrences in KJV Bible)
Transliteration:
naqam
Phonic:
naw-kam’
Meaning:
a primitive root; to grudge, i.e. avenge or punish
KJV Usage:
avenge(-r, self), punish, revenge (self), X surely, take vengeance