She inspired history of carbon and rising fossil fuel (4)
I believe the answer is:
clio
'she' is the definition.
'carbon and rising fossil fuel' is the wordplay.
'carbon' becomes 'C' (chemical symbol).
'and' means one lot of letters go next to another.
'rising' shows that the letters should be reversed in order (going up in a down clue).
'fossil fuel' becomes 'oil' (I've seen this before).
'oil' reversed gives 'lio'.
'c'+'lio'='CLIO'
'inspired history of' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for clio that I've seen before include "In Greek and Roman myth, the Muse of history" , "inspiration for historians" , "one historically inspiring" , "1 across's Muse - from Renault?" , "Muse of history - car" .)