Prince initially fancying small drink (4)
I believe the answer is:
Here is my best explanation:
'small drink' is the definition.
(e.g. a half pint)
'prince initially fancying' is the subsidiary indication.
'prince' becomes 'hal' (I've seen this in other clues**).
'initially' suggests taking the first letters.
The first letter of 'fancying' is 'f'.
(Other definitions for half that I've seen before include "proportion", "alcoholic drink", "Two of these to the pint", "Some football", "0.5", "Portion of bread (better than none?)", "Measure of beer", "One of two equal parts", "Fifty percent" and "Two of which make the whole".)