The most common and most likely answer to this crossword clue is the 7 letter word PUNJABI
I've seen this crossword clue in Independent
P
U
N
J
A
B
I
More clues leading to the result PUNJABI
- New injection I must follow up, turning back tongue
- Judge given notes in largely Carthaginian language
- Asian joke, one involving judge and sailor
- Language barrier initially faced by Poins after joke by Japanese-American
- Language of paper supporting sarcastic fellow leaving Punch
- Punch absorbed by Carthaginian cut tongue
- South Asian joke: dig one
- Tongue injection, one beyond a joke
- NB: Jaipur strangely has no rule for this language
- Witticism and dig I combined in Indian language
Buddy explains!

The straight part
We know that "Language" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case language = punjabi.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.