Loudly suggested rule has a shortcoming (4)
I believe the answer is:
flaw
'a shortcoming' is the definition.
(I've seen this in another clue)
'loudly suggested rule' is the wordplay.
'loudly' becomes 'f' (short for forte - 'loud' in music).
'suggested rule' becomes 'law' (law is a kind of rule. I am not sure about the 'suggested' bit.).
'f'+'law'='FLAW'
'has' acts as a link.
Can you help me to learn more?
(Other definitions for flaw that I've seen before include "Error in theory or plan" , "sudden rush" , "Defect, imperfection" , "Weakness" , "weak spot" .)