The most common and most likely answer to this crossword clue is the 9 letter word BOLSTERED
I've seen this crossword clue in The Daily Telegraph
B
O
L
S
T
E
R
E
D
More clues leading to the result BOLSTERED
Buddy explains!
The straight part
We know that "Given extra overnight support" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case given extra overnight support = bolstered.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 BOLSTERED mean?
BOLSTERED verb- To brace, reinforce, secure, or support.
- Padded