From BiblePortal Wikipedia

Vine's Expository Dictionary of OT Words [1]

Râdaph ( רָדַף , Strong'S #7291), “to pursue, follow after, pass away, persecute.” This verb also appears in Coptic, Syriac, Mandaean, Arabic, and postbiblical Aramaic. It appears in the Bible about 135 times and in all periods.

The basic meaning of this verb is “to pursue after” an enemy with the intent of overtaking and defeating him. In most of its occurrences râdaph is a military term. It first occurs in Gen. 14:14, where it is reported that Abram mustered his men ( אַחֳרֵן , Strong'S #318), men) and “pursued them [men who took his brother] unto Dan.” A nuance of this verb is “to pursue” a defeated enemy with the intent of killing him: “And he divided himself against them, he and his servants, by night, and smote them, and pursued them unto Hobah, which is on the left hand of Damascus” (Gen. 14:15). The one pursued is not always a hostile force—so Laban “took his brethren [army] with him, and pursued after him [Jacob] seven days’ journey; and they overtook him in the mount Gilead” (Gen. 31:23).

At times râdaph signifies pursuing without having a specific location or direction in mind, as in hunting for someone. This meaning is in 1 Sam. 26:20—David asked Saul why he was exerting so much effort on such an unimportant task (namely, pursuing him), “as when one doth hunt a partridge in the mountains.” The word occurs in Josh. 2:5, where Rahab tells the soldiers of Jericho: “… Whither the men [Israelite spies] went I wot not: pursue after them quickly; for ye shall overtake them.” This verse embodies the meaning first mentioned, but by Josh. 2:22 the emphasis has shifted to hunting, not intentional pursuit after an enemy whose location is known but a searching for an enemy in order to kill him: “And they went, and came unto the mountain, and abode there three days, until the pursuers were returned: and the pursuers sought them throughout all the way, but found them not.”

In another nuance râdaph can signify “to put to flight” or “to confront and cause to flee.” Moses reminded the Israelites that “the Amorites … came out against you, and chased you, as bees do, and destroyed you in Seir, even unto Hormah” (Deut. 1:44). Bees do not pursue their victims, but they certainly do put them to flight, or cause them to flee. In Josh. 23:10 Israel is reminded: “One man of you shall chase a thousand: for the Lord your God he it is that fighteth for you, as he hath promised you” (cf. Lev. 26:8).

Used in another sense, râdaph signifies the successful accomplishment of a pursuit; the pursuer overtakes the pursued but does not utterly destroy him (in the case of an army) and, therefore, continues the pursuit until the enemy is utterly destroyed. So Israel is warned of the penalty of disobedience to God: “The Lord shall smite thee with a consumption, and with a fever …; and they shall pursue thee until thou perish” (Deut. 28:22; cf. v. 45). This is the emphasis when God admonishes Israel: “That which is altogether just shalt thou follow, that thou mayest live, and inherit the land …” (Deut. 16:20); Israel is “to pursue” justice and only justice, as a goal always achieved but never perfected. They are to always have justice in their midst, and always “to pursue” it. This same sense appears in other figurative uses of the word: “Surely goodness and mercy shall follow me all the days of my life …” (Ps. 23:6; cf. Isa. 1:23; 5:11; Hos.6:3).

In a related meaning râdaph can signify “follow after.” This is not with any intention to do harm to the one pursued but merely “to overtake” him. So Gehazi “pursued” (followed after) Naaman, overtook him, and asked him for a talent of silver and two changes of clothes (2 Kings 5:21-22). The word also means “to follow after” in the sense of “practicing,” or following a leader: “They also that render evil for good are mine adversaries; because I follow the thing that good is” (Ps. 38:20; cf. 119:150; Prov. 21:21).

The third meaning of râdaph , “to persecute,” represents the constant infliction of pain or trouble upon one’s enemies. This meaning is seen in Deut. 30:7: “And the Lord thy God will put all these curses upon thine enemies, and on them that hate thee, which persecuted thee” (cf. Job 19:22, 28).

A special use of râdaph appears in Eccl. 3:15: “… God requireth [holds men accountable for] that which is past.” Men should serve God (literally, “fear him”) because God controls all things. Men should be on His side, since He is totally sovereign. The intensive stem sometimes means to pursue relentlessly and passionately as a harlot “pursues” her lovers (Prov. 11:19).

King James Dictionary [2]

Pursue, L sequor prosequor, or persequor. See Seek.

1. To follow to go or proceed after or in a like direction. The captain pursued the same course as former navigators have taken. A subsequent legislature pursued the course of their predecessors. 2. To take and proceed in, without following another. Captain Cook pursued a new and unexplored course. New circumstances often compel us to pursue new expedients and untried course. What course shall we pursue? 3. To follow with a view to overtake to follow with haste to chase as, to pursue a hare to pursue an enemy. 4. To seek to use measures to obtain as, to pursue a remedy at law. 5. To prosecute to continue. A stream proceeds from a lake and pursues a southerly course to the ocean.

He that pursueth evil, pursueth it to his own death.  Proverbs 11

6. To follow as an example to imitate.

The fame of ancient matrons you pursue.

7. To endeavor to attain to to strive to reach or gain.

We happiness pursue we fly from pain.

8. To follow with enmity to persecute.

This verb is frequently followed by after.  Genesis 35

Pursue To go on to proceed to continue a Gallicism.

I have, pursues Carneades, wondered chimists should not consider--

Webster's Dictionary [3]

(1): ( v. t.) To seek; to use or adopt measures to obtain; as, to pursue a remedy at law.

(2): ( v. t.) To proceed along, with a view to some and or object; to follow; to go in; as, Captain Cook pursued a new route; the administration pursued a wise course.

(3): ( v. t.) To prosecute; to be engaged in; to continue.

(4): ( v. t.) To follow as an example; to imitate.

(5): ( v. t.) To follow with enmity; to persecute; to call to account.

(6): ( v. i.) To go in pursuit; to follow.

(7): ( v. i.) To go on; to proceed, especially in argument or discourse; to continue.

(8): ( v. i.) To follow a matter judicially, as a complaining party; to act as a prosecutor.

(9): ( v. t.) To follow with a view to overtake; to follow eagerly, or with haste; to chase; as, to pursue a hare.

Vine's Expository Dictionary of NT Words [4]

1: Διώκω (Strong'S #1377 — verb — dioko — dee-o'-ko )

"to put to flight, pursue, persecute," is rendered "to pursue" in  2—Corinthians 4:9 , RV (AV, "persecute"), and is used metaphorically of "seeking eagerly" after peace in  1—Peter 3:11 , RV (AV, "ensue"). See Follow.