After a cold, there's something slippery about that woman exhibiting weakness (8,4)
I believe the answer is:
achilles heel
'weakness' is the definition.
(I've seen this before)
'after a cold there's something slippery about that woman' is the wordplay.
I cannot quite understand how this works, but
'a' is present in the answer.
'cold' could be 'chill' (chill is a kind of cold) and 'chill' is found within the answer.
'woman' could be 'she' and 'she' is found within the answer.
The remaining letters 'eel' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).
'exhibiting' is the link.
Can you help me to learn more?
(Other definitions for achilles heel that I've seen before include "Small but crucial weakness" , "Personal weak spot" , "flaw" , "One's most vulnerable spot" , "Only vulnerable point" .)