Put down ... Queen Ursula starts to like Hat Head (5)
'put down' is the definition.
(I've seen this before)
'queen ursula starts to like hat head' is the wordplay.
'starts to' suggests taking the first letters.
'like' becomes 'as'.
'head' says to take the initial letters.
The first letters of 'queen ursula' is 'qu'.
The initial letter of 'hat' is 'h'.
(Other definitions for quash that I've seen before include "Invalidate", "Subdue", "Overturn (judgment)", "Suppress -- annul", "Suppress or crush, say a rebellion".)