One's tight covering of bandage material is out of the ordinary (9)
I believe the answer is:
skinflint
'one's tight' is the definition.
(I know that skinflint are mean)
'covering of bandage material is out of the ordinary' is the wordplay.
I cannot really understand how this works, but
'covering' could be 'skin' (skin is a kind of covering) and 'skin' is found within the answer.
'material' could be 'flint' (flint is a kind of material) and 'flint' is found within the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for skinflint that I've seen before include "cheapskate" , "A miserly person like Scrooge" , "Very ungenerous or stingy person" , "A miserly person, tightwad" , "Scrooge, miser" .)