Care about right tendency (5)
I believe the answer is:
trend
'tendency' is the definition.
(I know that tendency can be written as trend)
'care about right' is the wordplay.
'care' becomes 'tend' (I've seen this in other clues).
'about' is an insertion indicator.
'right' becomes 'r' (common abbreviation).
'tend' placed around 'r' is 'TREND'.
(Other definitions for trend that I've seen before include "Drift; vogue" , "Fashion; general drift" , "General tendency" , "General direction in which something is developing" , "General direction of change" .)