Princess hugging uni graduate in sheikhdom (5)
I believe the answer is:
dubai
'sheikhdom' is the definition.
(I've seen this before)
'princess hugging uni graduate' is the wordplay.
'princess' becomes 'di' (Princess Diana).
'hugging' is an insertion indicator (outside letters hug or embrace inside letters).
'uni' becomes 'u' (U is an abbreviation for university).
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'u'+'ba'='uba'
'di' going around 'uba' is 'DUBAI'.
'in' acts as a link.
(Other definitions for dubai that I've seen before include "Arab city" , "Persian Gulf state" , "Gulf territory" , "Port city on the Persian Gulf" , "One of the UAE and its capital" .)