Mistake made by little brat losing head (5)
I believe the answer is:
error
'mistake' is the definition.
(synonyms)
'little brat losing head' is the wordplay.
'little brat' becomes 'terror' (I've seen this before).
'losing head' means to remove the first letter.
'terror' with its first letter taken off is 'ERROR'.
'made by' acts as a link.
(Other definitions for error that I've seen before include "Mistake or fault" , "Faulty judgment" , "Howler" , "Mistake from terrorist" , "Slip-up" .)