Forgive

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Old English forgiefan, of Germanic origin, related to Dutch vergeven and German vergeben, and ultimately to for- and give.

wiktionary

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Alternation (due to give) of Middle English foryiven, forȝiven, from Old English forġiefan(“to forgive, give up, provide”), from Proto-Germanic *fragebaną(“to give away; give up; release; forgive”), equivalent to for- +‎ give (etymologically for- + yive). Cognate with Scots forgeve, forgif, forgie(“to forgive”), West Frisian ferjaan(“to forgive”), Dutch vergeven(“to forgive”), German vergeben(“to forgive”), Icelandic fyrirgefa(“to forgive”).

etymonline

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forgive (v.)

Old English forgiefan "give, grant, allow; remit (a debt), pardon (an offense)," also "give up" and "give in marriage" (past tense forgeaf, past participle forgifen); from for-, here probably "completely," + giefan "to give" (from PIE root *ghabh- "to give or receive").

The sense of "to give up desire or power to punish" (late Old English) is from use of such a compound as a Germanic loan-translation of Vulgar Latin *perdonare (Old Saxon fargeban, Dutch vergeven, German vergeben "to forgive," Gothic fragiban "to grant;" and see pardon (n.)). Related: Forgave; forgiven; forgiving.