Exclamation of surprise -- gin running short (Queen's favourite?) (5)
I believe the answer is:
corgi
'queen's favourite?' is the definition.
(I've seen this before)
'exclamation of surprise gin running short' is the wordplay.
'exclamation of surprise' becomes 'cor' (expression of surprise).
'running short' means to remove the last letter.
'gin' with its final letter taken away is 'gi'.
'cor'+'gi'='CORGI'
(Other definitions for corgi that I've seen before include "pet in 9 [CARDIFF]?" , "The Queen's favourite?" , "Small Welsh dog with fox-like head" , "Pre-2018 royal dog" , "One of the Queen's dogs?" .)