Liable to show an upsurge in nepotism (4)
I believe the answer is:
open
'liable' is the definition.
(thesaurus)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for open that I've seen before include "Traditional room heater" , "Allowing access" , "with no clear favourite" , "golf contest" , "Not enclosed" .)