The most common and most likely answer to this crossword clue is the 6 letter word ANDEAN
I've seen this crossword clue in Financial Times
A
N
D
E
A
N
More clues leading to the result ANDEAN
- An academic or clergyman from South America
- Article on churchman from a range
- A new cleric from South America
- Dan and Ena ramble about S. American mountain range
- A new faculty head from the highlands?
- Retired editor sent in articles from long range
- Concerning a specific chain of thought one lost when girl’s around
- An Anglican clergyman peaking in South America?
- Answer to new clergyman in Peak District
- Name held by a dignitary pertaining to chain
Buddy explains!

The straight part
We know that "in Peak District" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in peak district = andean.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.