Having broken desk, theologian (in drink) to make quick getaway (9)
I believe the answer is:
skedaddle
'make quick getaway' is the definition.
(skedaddle can mean to run away)
'having broken desk theologian in drink' is the wordplay.
'having broken' is an anagram indicator.
'theologian' becomes 'dd' (Doctor of Divinity degree).
'in' is an insertion indicator.
'drink' becomes 'ale' (ale is a kind of drink).
'dd' inserted inside 'ale' is 'addle'.
'desk' anagrammed gives 'sked'.
'sked'+'addle'='SKEDADDLE'
'to' acts as a link.
(Other definitions for skedaddle that I've seen before include "Bunk off quickly!" , "take flight" , "Run off hurriedly (colloq.)" , "Depart hurriedly" , "Get out of town!" .)