If you want the clinical definition, you'll need the criteria as described in the DSM; there are a number of them that must be satisfied in order for one to be diagnosed officially with NPD.
Then again, you don't need a weatherman to know which way the wind blows. My ex was a narcissist, because she effortlessly displayed these egregious mental defects easily:
Lack of empathy
Belief that one is "special" and deserves special treatment
Lack of self-awareness(this is not limited to NPD)
Need for excessive(usually unwarranted) admiration
They love bomb, they lie, they control, they gaslight. Run afoul of them and you'll get the "silent treatment" to "punish" you. They fucking suck and are trash people(that is not in the DSM but probably should be).
https://www.mayoclinic.org/diseases-conditions/narcissistic-personality-disorder/symptoms-causes/syc-20366662
Sadly, though, as in most cases of mental illness, knowing what makes them tick does absolutely NOTHING. They think that everyone else has the problem, so they will never get better.
No judgment, cause I was the dumbass who hung in there for 6 years until I realized I was stuck in a cyclical pattern of up/down, gain/loss. There are different types of narcs, but they largely do and say all the same stupid shit. It's actually a little terrifying.