The most common and most likely answer to this crossword clue is the 11 letter word OBSERVATORY
I've seen this crossword clue in The Times
O
B
S
E
R
V
A
T
O
R
Y
More clues leading to the result OBSERVATORY
Buddy explains!
The straight part
We know that "where stars are looked for" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where stars are looked for = observatory.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 OBSERVATORY mean?
OBSERVATORY noun- A place where stars, planets and other celestial bodies are observed, usually through a telescope; also place for observing meteorological or other natural phenomena.
- A lookout (vantage point with a view of the surrounding area)