Quiet tear about Mike reveals weak character (6)
I believe the answer is:
shrimp
'weak character' is the definition.
(shrimp can mean a weak or puny person)
'quiet tear about mike' is the wordplay.
'quiet' becomes 'sh' (both can be said to tell someone to be quiet).
'tear' becomes 'rip' (ripping is a kind of tearing).
'about' is an insertion indicator.
'mike' becomes 'M' (phonetic alphabet: alpha, bravo, charlie etc.).
'rip' going around 'm' is 'rimp'.
'sh'+'rimp'='SHRIMP'
'reveals' acts as a link.
(Other definitions for shrimp that I've seen before include "Raising of a siege" , "School member" , "Diminutive person" , "tiny fellow!" , "Tot" .)