The most common and most likely answer to this crossword clue is the 5 letter word FLING
I've seen this crossword clue in The Guardian
F
L
I
N
G
More clues leading to the result FLING
- Fellow's beginning with Heather in hasty romance
- Affair takes one out of office work
- Try brief relationship
- Casual affair, as steps taken in Scotland?
- Shy affair
- Cast of Brief Encounter
- Affair with female swimmer
- An affair, possibly a Scottish country dance
- Cast for fine fish
- I must quit office job, being shy
Buddy explains!

The straight part
We know that "Cast/Brief Encounter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cast/brief encounter = fling.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 FLING mean?
FLING noun- An act of throwing, often violently.
- An act of moving the limbs or body with violent movements, especially in a dance.
- An act or period of unrestrained indulgence.
- A short casual sexual relationship.
- An attempt, a try (as in "give it a fling").
- A severe or contemptuous remark; an expression of sarcastic scorn; a gibe or taunt.
- A lively Scottish country dance.
- A trifling matter; an object of contempt.
- To move (oneself) abruptly or violently; to rush or dash.
- To throw with violence or quick movement; to hurl.
- To throw; to wince; to flounce.
- To utter abusive language; to sneer.