Eastern riots becoming serious (7)
I believe the answer is:
earnest
'serious' is the definition.
('earnest' can be similar in meaning to 'serious')
'eastern riots' is the wordplay.
'riots' indicates anagramming the letters.
'eastern' is an anagram of 'EARNEST'.
'becoming' acts as a link.
(Other definitions for earnest that I've seen before include "Eastern (anag.)" , "Sincere, solemn" , "Serious, solemn" , "Serious - money deposit" , "Grave" .)