It's true, miser will abandon case when they become aware of it (7)
I believe the answer is:
realise
'abandon case when they become aware of it' is the definition.
The definition suggests an adverb but the answer is not.
'it's true miser' is the wordplay.
'it's true' becomes 'real' (synonyms).
'miser' becomes 'ise' (I can't explain this - if you can you should give a lot more credence to this answer).
'real'+'ise'='REALISE'
'will' is the link.
Can you help me to learn more?
(Other definitions for realise that I've seen before include "Turn into cash; come to see" , "Discover" , "catch on" , "Become aware of; fulfil (S, not Z)" , "Bring to fruition" .)