The most common and most likely answer to this crossword clue is the 7 plus 7 letter word PARTIAL ECLIPSE
I've seen this crossword clue in The Sunday Telegraph
P
A
R
T
I
A
L
E
C
L
I
P
S
E
More clues leading to the result PARTIAL ECLIPSE
- Awfully ill, appreciates incomplete coverage – seen as ominous by some
- Drink after first piece reduces energy — that limits star’s appearance
- and 21 Down: Coming across to dim the light
- Incomplete screening — biased excerpt from the clip seen
- Phenomenon seen in clips?
- Section one: all pieces created in a natural phenomenon
Buddy explains!
The straight part
We know that "that limits star’s appearance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that limits star’s appearance = partial eclipse.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.