Emergence of a challenger to dictator (7)
I believe the answer is:
arrival
'emergence' is the definition.
(thesaurus)
'a challenger to dictator' is the wordplay.
'a challenger' becomes 'rival' ('rival' can be a synonym of 'challenger').
'to' says to put letters next to each other (I've seen this in other clues).
'dictator' becomes 'ar' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'rival' put after 'ar' is 'ARRIVAL'.
'of' acts as a link.
(Other definitions for arrival that I've seen before include "Appearance (at a place)" , "Someone who's just come" , "Act of coming" , "Attainment of destination" , "Entry" .)