[intransitive] to be a candidate in an election for a political position, especially in the US
Bush ran a second time in 2004.
run for somebody/something to run for president
run in something to run in the election
Source: http://www.oxfordlearnersdictionaries.com/definition/english...

"The most important step that he can take is to address his nation and declare that neither he nor the son he has been positioning as his successor will run in the presidential election this year," Mr Kerry writes.
Source: http://news.bbc.co.uk/2/hi/middle_east/9384085.stm

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Note added at 1 day3 hrs (2016-10-01 14:45:25 GMT)
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It might be more accurate to translate it as "run for the presidential election" because it is للانتخابات, not في الانتخابات.

I was a bit surprised to learn that the United States, considered here as a model of multiculturalism, still forbids “former foreigners” to run for the presidential election.
Source: http://www.huffingtonpost.com/sabine-hervy/eva-joly-election...