King the writer's accepted by international Adriatic resort (6)
I believe the answer is:
'adriatic resort' is the definition.
(I've seen this before)
'king the writer's accepted by international' is the wordplay.
'king' becomes 'R' (abbreviation for rex, king in Latin).
'the writer's' becomes 'I'm' ('I am' referring to the writer of the clue).
'accepted' becomes 'in' (I've seen this in other clues).
'by' means one lot of letters go next to another.
'international' becomes 'i' (abbreviation eg in IMF).
(Other definitions for rimini that I've seen before include "N. Italian city" , "Italian holiday resort" , "Italian place" , "Francesca's place" , "Italian coastal city" .)