Fuel is a favourite outside (4)
I believe the answer is:
peat
'fuel' is the definition.
(peat is a kind of fuel)
'a favourite outside' is the wordplay.
'favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
'outside' means one lot of letters goes inside another.
'a' going within 'pet' is 'PEAT'.
'is' acts as a link.
(Other definitions for peat that I've seen before include "load of stuff in the garden?" , "Fuel dug from bog" , "Decomposed vegetable matter" , "Organic fuel" , "Tape (anag.)" .)