Minor hang-up (4)
I believe the answer is:
snag
'minor hang-up' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for snag that I've seen before include "Tear - catch" , "Hidden drawback; tear" , "Jagged projection" , "Disadvantage - small hole in fabric" , "banger down under" .)