The most common and most likely answer to this crossword clue is the 6 plus 9 letter word COUNTY FERMANAGH
I've seen this crossword clue in The Times
C
O
U
N
T
Y
F
E
R
M
A
N
A
G
H
Buddy explains!
The straight part
We know that "Part of Ulster" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of ulster = county fermanagh.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.