The most common and most likely answer to this crossword clue is the 8 letter word DRIPPING
D
R
I
P
P
I
N
G
More clues leading to the result DRIPPING
Buddy explains!

The straight part
We know that "Fat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fat = dripping.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does DRIPPING mean?
DRIPPING verb- To fall one drop at a time.
- To leak slowly.
- To let fall in drops.
- (usually with with) To have a superabundance of valuable things.
- (of the weather) To rain lightly.
- To be wet, to be soaked.
- To whine or complain consistently; to grumble.
- Solid animal fat, traditionally collected from dripping off roasting meat.
- The sound or action of something that drips.
- The use of a drip tip to drip e-liquid directly onto the atomizer of an e-cigarette.