Fuel to run a pet (4)
I believe the answer is:
peat
'fuel' is the definition.
(peat is a kind of fuel)
'run a pet' is the wordplay.
'run' is an anagram indicator (I've seen this in other clues).
'a'+'pet'='apet'
'apet' with letters rearranged gives 'PEAT'.
'to' is the link.
(Other definitions for peat that I've seen before include "Form of fuel" , "load of stuff in the garden?" , "Fuel cut from bog" , "Fuel dug from bog" , "Saturated and compressed vegetable matter, used as fuel when dried out" .)