Cryptic crossword clue
I appreciate that time is short for director

The most common and most likely answer to this crossword clue is the 4 letter word TATI

I've seen this crossword clue in Independent
T
A
T
I

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

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