The most common and most likely answer to this crossword clue is the 10 letter word FLICKERING
I've seen this crossword clue in The Times
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Buddy explains!

The straight part
We know that "making brief appearance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case making brief appearance = flickering.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 FLICKERING mean?
FLICKERING verb- To burn or shine unsteadily, or with a wavering light.
- To keep going on and off; to appear and disappear for short moments; to flutter.
- To flutter; to flap the wings without flying.
- A short, uncertain burst.
- Shining unsteadily or vary rapidly in brightness (referring to a light or a source of light)