to become angry easily.
A wrestling/grappling term for applying a submission hold or lock on an opponent — used in lucha libre, judo, and jiu-jitsu alike: le agarró llave al brazo. Llave here means 'hold/lock,' not a literal key; outside combat sports, the phrase doesn't carry a separate meaning.
Taking llave literally as 'key' — in this fixed sports phrase it means a grappling hold or lock, a completely different, unrelated sense of the word.
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"agarrar llave" means "to become angry easily.".