Tourist centre in Dover -- is riot developing? (7)
I believe the answer is:
visitor
'tourist' is the definition.
(eg a visitor to another country)
'centre in dover is riot developing?' is the wordplay.
'centre in' means to look at the middle letters.
'developing?' indicates anagramming the letters (letters developed into a new form).
The middle letter of 'dover' is 'v'.
'riot' with letters rearranged gives 'itor'.
'v'+'is'+'itor'='VISITOR'
(Other definitions for visitor that I've seen before include "Guest - tourist" , "Caller, guest" , "Seasonal migratory bird" , "who might stay?" , "Person turning up" .)