AA rung last: desperate to obtain fuel (7,3)
I believe the answer is:
natural gas
'fuel' is the definition.
(I know that natural gas is a type of fossil fuel)
'aa rung last desperate' is the wordplay.
'desperate' indicates anagramming the letters (a desperate or pathetic spelling).
'aa'+'rung'+'last'='aarunglast'
'aarunglast' with letters rearranged gives 'NATURAL GAS'.
'to obtain' acts as a link.
(Other definitions for natural gas that I've seen before include "Energy source from underground" , "Fuel from underground" , "Fuel from eg 2 down" .)