The most common and most likely answer to this crossword clue is the 4 plus 3 letter word REEL OFF
I've seen this crossword clue in The Guardian
R
E
E
L
O
F
F
More clues leading to the result REEL OFF
- Stagger race start and run through quickly?
- Stagger away, say, without apparent effort
- Quickly go through angler’s problem?
- Uncertain feel for list
- Take a lecherous look back at Dicky and give a faultless recitation
- Quickly, list some conger eel offcuts
- Quickly run through king, escape back round old wharf finally
- Dance away, say, without apparent effort
- Announce with speed and fluency: ‘Dance cancelled’
- Thus unable to show film list
Buddy explains!

The straight part
We know that "Quickly run through" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quickly run through = reel off.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.