The most common and most likely answer to this crossword clue is the 9 letter word ANOMALOUS
I've seen this crossword clue in The Times
A
N
O
M
A
L
O
U
S
More clues leading to the result ANOMALOUS
- Irregular old lady new union saloon lets in
- Right sacrificed by a regular old American — that’s exceptional
- Old woman, behold, in a sense peculiar
- An old malicious heartless oddball
- Eccentric soul madly pursuing an unclothed woman
- Unusual moan a soul let loose
- Unusual answer not entirely bad following denial by mother
- Irregular sections of another male louse
- Badly translated old manual so eccentric
- Nothing in a loan sum that’s out of order or exeptional
Buddy explains!

The straight part
We know that "peculiar" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case peculiar = anomalous.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 ANOMALOUS mean?
ANOMALOUS adjective- Deviating from the normal; marked by incongruity or contradiction; aberrant or abnormal.
- Of uncertain or unknown categorization; strange.
- Having anomalies.