The most common and most likely answer to this crossword clue is the 5 plus 5 letter word FALSE TEETH
I've seen this crossword clue in Independent
F
A
L
S
E
T
E
E
T
H
More clues leading to the result FALSE TEETH
- He left a fluid around badger’s home: they might come out at night?
- Brief tumble with Henry on settee broke dentures
- Fine-tuned athletes, packed with energy, taken out at night?
- Reassembled fleet with haste set out at night
- They may be in for supper but then out all night
- Empty fable, the tale that’s contrived about stars primarily, those coming out at night
- Fleet deployed with haste — such must come out at night
- Those on bridge perhaps as the fleet is scuttled
- Fitted pegs?
- Note steel construction shaped the prosthetics
Buddy explains!

The straight part
We know that "set out at night" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case set out at night = false teeth.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.