The phrase "first primary debate" refers to the initial or very first debate among candidates from the same political party who are running to become their party's nominee or representative in an upcoming election. Full definition
They face off in our first primary debate on Time Warner Cable News. (spectrumlocalnews.com)
Typically, the first primary debate is seen as the official start of the campaign season. (ny1.com)
Democratic 2016 frontrunner Hillary Clinton revealed the night of her party's first primary debate was the same night her granddaughter, Charlotte, called her «grandma» for the first time. (nystateofpolitics.com)