Princess in straying goes for silver -- that's pushiness (10)
I believe the answer is:
aggression
'pushiness' is the definition.
(thesaurus)
'princess in straying goes for silver' is the wordplay.
I cannot really understand how this works, but
'silver' could be 'ag' (Ag is the chemical symbol for silver) and 'ag' is located in the answer.
This explanation may well be incorrect...
'that's' acts as a link.
Can you help me to learn more?
(Other definitions for aggression that I've seen before include "Hostile action" , "Act of hostility" , "Violent hostility" , "warlike attitude" , "Act of aggression,physical force" .)