The most common and most likely answer to this crossword clue is the 7 plus 3 letter word HAULIER (A)
H
A
U
L
I
E
R
(
A
)
Buddy explains!
The straight part
We know that "indulgence as of old in these parts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case indulgence as of old in these parts = haulier (a).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.