Drink last of spirits with determination (5)
I believe the answer is:
swill
'drink' is the definition.
(swilling is a kind of drinking)
'last of spirits with determination' is the wordplay.
'last of' says to take the final letters.
'with' is a charade indicator (letters next to each other).
'determination' becomes 'will' (I've seen this before).
The last letter of 'spirits' is 's'.
's'+'will'='SWILL'
(Other definitions for swill that I've seen before include "Pig-food; rinse" , "Hogwash" , "Pigfeed" , "Wet pig feed" , "Pigs' food" .)