He 'campaigned for president/governor/mayor'. = He 'campaigned' for the presidency/governorship/mayoralty. [=he tried to be elected president/governor/mayor]
The group launched/mounted/led a 'campaign' to protect the area from commercial development.
The university is organizing a 'campaign' to attract a more diverse student population.
(..) before Ser Jorah seized that role for himself. Jorah sent my secrets to Varys. For years the Spider oversaw the campaign to find and kill me. He did what he had to do to survive. He did a lot of other things as well, things he didn't have to do. But you trust him? (..)2015 TvShow: Game of Thrones Title: Hardhome Season: 5 Episode 8