Shake badly-behaved child held by rival (7)
I believe the answer is:
vibrate
'shake' is the definition.
(I know that shake is a more specific form of the action the vibrate)
'badly-behaved child held by rival' is the wordplay.
'badly behaved child' becomes 'brat' (I've seen this before).
'held by' indicates putting letters inside.
'rival' becomes 'vie' (I've seen this in other clues).
'brat' placed into 'vie' is 'VIBRATE'.
(Other definitions for vibrate that I've seen before include "Move rapidly to and fro" , "Oscillate rapidly" , "tremble" , "Quiver rapidly, resonate" , "swing" .)