Smallest amount of gin and relative's wasted (5)
I believe the answer is:
gaunt
'wasted' is the definition.
(I know that wasted can be written as gaunt)
'smallest amount of gin and relative's' is the wordplay.
'smallest amount of' suggests taking the first letters.
'and' means one lot of letters go next to another.
'relative' becomes 'aunt' (aunt is a type of relative).
The first letter of 'gin' is 'g'.
'g'+'aunt'='GAUNT'
(Other definitions for gaunt that I've seen before include "Unhealthily thin" , "forlorn" , "place associated with Edward III's son" , "Very slight" , "birthplace of Edward's son" .)