The most common and most likely answer to this crossword clue is the 7 letter word ADIPOSE
A
D
I
P
O
S
E
More clues leading to the result ADIPOSE
- Fat girl with an attitude going about
- Fatty Arbuckle, initially poised, cracks up
- Points to a ring around sink resembling fat
- Fat duke and I entertained by a model
- Fatty‘s ideas for exercise — drinking a lot of soda
- Notice one model getting fat
- Fatty, a pickpocket, got up right away
- Fat Teletubby introduced to crazy aides
- Fatty requires active duty shortly, I suggest
- Fat and foolish, said Poe
Buddy explains!

The straight part
We know that "fatty material" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fatty material = adipose.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 ADIPOSE mean?
ADIPOSE noun- Animal fat stored in the tissue of the body.
- Containing, composed of, or consisting of fat; fatty.
- Slightly overweight; chubby.