This keeps a tight hold on immorality (4)
I believe the answer is:
vice
'immorality' is the definition.
(vice can mean immoral behaviour)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for vice that I've seen before include "Wicked habit" , "may have a powerful grip" , "Fault - gripping tool" , "One that grips" , "Immorality; clamping device" .)