primarying

verb
  1. 1

    To challenge (an incumbent sitting politician) for their political party's endorsement to run for re-election, through running a challenger campaign in a primary election, especially one that is more ideologically extreme.

  2. 2

    To take part in a primary election.

noun
  1. 1

    Mounting a challenge to an incumbent office-holder in a party primary.

Source: https://en.wiktionary.org/wiki/primary, https://en.wiktionary.org/wiki/primarying