The most common and most likely answer to this crossword clue is the 8 letter word APPESTAT
I've seen this crossword clue in Independent
A
P
P
E
S
T
A
T
Buddy explains!

The straight part
We know that "part of brain" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of brain = appestat.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 APPESTAT mean?
APPESTAT noun- The area of the brain (possibly in the hypothalamus) supposed to control appetite and regulate food intake