New parts where Riviera is improving (2,3,4)
I believe the answer is:
on the mend
'improving' is the definition.
(I've seen this before)
'new parts where riviera is' is the wordplay.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'parts' indicates putting letters inside (in the sense of cuts or separates).
'where riviera is' becomes 'on the Med' (the French Riviera is on the Mediterranean coast).
'n' placed into 'onthemed' is 'ON THE MEND'.
(Other definitions for on the mend that I've seen before include "Informally getting better, improving after illness or accident" , "convalescing" , "returning to health" , "undergoing recovery?" , "Becoming better in health" .)