Extremely tipsy drinking rum, an alcoholic beverage (5)
I believe the answer is:
toddy
'an alcoholic beverage' is the definition.
(I've seen this before)
'extremely tipsy drinking rum' is the wordplay.
'extremely' suggests removing the centre.
'drinking' means one lot of letters goes inside another.
'rum' becomes 'odd' (I've seen this before).
'tipsy' with its centre removed is 'ty'.
'ty' placed around 'odd' is 'TODDY'.
(Other definitions for toddy that I've seen before include "Mixture of spirits, sugar and hot water" , "Warm alcoholic drink" , "Hot alcoholic drink" , "Hot drink of spirits with sugar and spices" , "Hot drink of alcohol" .)