用人唯親 in English is called nepotism, meaning you give unfair advantage to your own family if you are in a position of power, especially by giving them jobs.  But if you give jobs to someone who is able and sagacious regardless of whether he or she is your next of kin or not, then that is 內舉不避親.

Well, being able and sagacious is a prerequisite to 內舉 , but subject to public recognition.  With this standard, Chiang ching-kuo is acceptable though he is the son and heir of Chiang Kai-shek.  Okay, let's just wait and see if Wonky Cai's cousin is qualified to take up the post of Labor Affairs.  (Maybe she doesn't need to prove it at all.) 

P.S.  You may argue that President Xi Jinping is also a princeling of a CCP elder.  That's quite different.  Xi's father had no absolute power in CCP, and when Xi was promoted to the top post, his father had been long gone.  In fact, after long journey through crucibles, Xi acquired the "job" in his own right.