The most common and most likely answer to this crossword clue is the 10 plus 1 plus 1 letter word HINDUSTANI - A
I've seen this crossword clue in The Times
H
I
N
D
U
S
T
A
N
I
-
A
Buddy explains!
The straight part
We know that "Delhi dialect" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case delhi dialect = hindustani - 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.