Graduate meeting royalty unexpectedly in town office (9)
I believe the answer is:
mayoralty
'town office' is the definition.
'graduate meeting royalty unexpectedly' is the wordplay.
'graduate' becomes 'ma' (abbreviation for Master of Arts).
'meeting' is a charade indicator (letters next to each other).
'unexpectedly' indicates anagramming the letters.
'royalty' anagrammed gives 'yoralty'.
'ma'+'yoralty'='MAYORALTY'
'in' is the link.
(Other definitions for mayoralty that I've seen before include "Henchard's office" , "elected office" , "civic office" , "Top town hall office" , "public office" .)