Prince initially fancying small drink (4)
I believe the answer is:
half
'small drink' is the definition.
(e.g. a half pint)
'prince initially fancying' is the wordplay.
'prince' becomes 'hal' (I've seen this before).
'initially' indicates taking the first letters.
The initial letter of 'fancying' is 'f'.
'hal'+'f'='HALF'
(Other definitions for half that I've seen before include "Portion of bread (better than none?)" , "Two of these to the pint" , "Fifty percent" , "Measure of beer" , "One of two equal parts" .)