Crate broke a little bit (5)
I believe the answer is:
trace
'a little bit' is the definition.
(a trace is a small amount)
'crate broke' is the wordplay.
'broke' indicates an anagram.
'crate' with letters rearranged gives 'TRACE'.
(Other definitions for trace that I've seen before include "Discover; remains" , "Pinch" , "Vestige, hint" , "Scarcely detectable amount" , "Seek out" .)