Meagre as everything short and fat (6)
I believe the answer is:
'fat' is the definition.
(animal fat for cooking)
'meagre as everything short' is the wordplay.
'meagre' becomes 'gre' (I can't justify this - if you can you should believe this answer much more).
'short' indicates taking the first letters.
The first letter of 'everything' is 'e'.
'and' is the link.
Can you help me to learn more?
(Other definitions for grease that I've seen before include "A thick oily substance" , "Musical - lubricant" , "Travolta's 1978 film" , "Lubricate (-ant)" , "bribe" .)