The most common and most likely answer to this crossword clue is the 6 letter word CORTEX
C
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R
T
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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 = cortex.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 CORTEX mean?
CORTEX noun- The outer layer of an internal organ or body structure, such as the kidney or the brain.
- The tissue of a stem or root that lies inward from the epidermis, but exterior to the vascular tissue.