Drunk ends your beginning (5)
I believe the answer is:
tipsy
'drunk' is the definition.
(thesaurus)
'ends your beginning' is the wordplay.
'ends' becomes 'tips' (tip is a kind of end).
'beginning' suggests taking the first letters.
The initial letter of 'your' is 'y'.
'tips'+'y'='TIPSY'
(Other definitions for tipsy that I've seen before include "Slightly intoxicated" , "Loaded" , "Inebriated" , "1 over 8" , "Rather drunk" .)