Keep quiet, depressed after tweet (4,4)
I believe the answer is:
pipe down
'keep quiet' is the definition.
(to pipe down is to be quiet)
'depressed after tweet' is the wordplay.
'depressed' becomes 'down' (synonyms).
'after' says to put letters next to each other.
'tweet' becomes 'pipe' (both can mean to make a high-pitched sound).
'down' after 'pipe' is 'PIPE DOWN'.
(Other definitions for pipe down that I've seen before include "Sh!" , "Be quiet!" , "Stop talking" , "Shut up!" , "Say no more!" .)