The most common and most likely answer to this crossword clue is the 13 letter word SHORT-SIGHTED
I've seen this crossword clue in Independent
S
H
O
R
T
-
S
I
G
H
T
E
D
Buddy explains!

The straight part
We know that "improvident" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case improvident = short-sighted.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 SHORT-SIGHTED mean?
SHORT-SIGHTED adjective- Near-sighted; myopic; unable to focus on distant objects.
- Unable to see long-term objectives; lacking foresight.