The most common and most likely answer to this crossword clue is the 2 plus 3 letter word ID EST
I've seen this crossword clue in Independent
I
D
E
S
T
More clues leading to the result ID EST
- Fateful date: the 6th of August, to be specific
- That is the thing about some in France
- Day in Rome, time that is in local parlance
- That’s one place to go, briefly
- Part of inside story that is translated
- I stop eliminating lives, in other words
- That is a date in Rome – September the fourth
- That is part of bride’s trousseau
- A date in March to beware – and time, that is
- Superlative broad
Buddy explains!

The straight part
We know that "that is in local parlance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that is in local parlance = id est.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.