If something has a higher priority than something else, it takes precedence. It does not take precedent. If you write that, you will look foolish.
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Our first Mind Your Language column for 2014 comes from the same "I didn't hear that phrase correctly and now I'm using the wrong version" school that also leads to such clangers as 'loose your mind' and 'make due'. That doesn't stop the wrong version popping up in professional contexts, such as this news report. There are also plenty of examples of 'precedence' being used when 'precedent' is the correct choice.
Per the Macquarie Dictionary, precedent means "a preceding instance or case". Precedence means "the act or fact of preceding". If you can't confidently distinguish the two versions, don't use either. Accuracy matters.
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.