Concerning story some caveats soften (7)
I believe the answer is:
relieve
'soften' is the definition.
(thesaurus)
'concerning story some caveats' is the wordplay.
'concerning' becomes 're' (both can mean on a particular topic).
'story' becomes 'lie' (story can mean a fabrication).
'some caveats' becomes 've' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
're'+'lie'+'ve'='RELIEVE'
Can you help me to learn more?
(Other definitions for relieve that I've seen before include "Take place of" , "Soothe" , "Free someone from duty by taking his place" , "Free from obligation" , "Alleviate pain or stress" .)