Rent a place on the Adriatic (5)
I believe the answer is:
split
'rent' is the definition.
(rent can mean split or torn)
'a place on the adriatic' is the wordplay.
'a place' becomes 'pl' (abbreviation used in postal addresses).
'on' indicates putting letters inside.
'the adriatic' becomes 'sit' (I can't justify this - if you can you should give a lot more credence to this answer).
'pl' inserted into 'sit' is 'SPLIT'.
Can you help me to learn more?
(Other definitions for split that I've seen before include "Divided" , "Mediterranean port" , "share out" , "run away" , "Divide; leave suddenly" .)