The most common and most likely answer to this crossword clue is the 4 letter word HIED
I've seen this crossword clue in The Guardian
H
I
E
D
Buddy explains!

The straight part
We know that "Hastened" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hastened = hied.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 HIED mean?
HIED verb- To hasten; to go quickly, to hurry.
- To hurry (oneself).