Story that might be current? (7)
I believe the answer is:
account
'story' is the definition.
(synonyms)
'might be current?' is the wordplay.
I cannot quite understand how this works, but
'be' could be 'count' (counting is a kind of being) and 'count' is found within the answer.
'current?' could be 'ac' (alternating current) and 'ac' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
'that' acts as a link.
Can you help me to learn more?
(Other definitions for account that I've seen before include "Invoice - story" , "History" , "Profitable to turn to this" , "Report of an event" , "Bank record" .)