The phrase "to fight the election" means to participate in a competition to win votes and be elected as a leader or representative in a political position. Full definition
And we can not fight election campaigns pretending that we are not in government. (politics.co.uk)
With this reality, the temptation to join the gravy train is overwhelming — and to fight elections as if life depends on it. (blog.politics.ox.ac.uk)
Those supporting a convention say that to fight the election of delegates supported by groups they oppose, they plan to recruit, train and run a slate of delegates of their own. (timesunion.com)