The most common and most likely answer to this crossword clue is the 10 letter word STAFFROOMS
I've seen this crossword clue in The Times
S
T
A
F
F
R
O
O
M
S
More clues leading to the result STAFFROOMS
Buddy explains!
The straight part
We know that "Form of SATs bandied about in these?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case form of sats bandied about in these? = staffrooms.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 STAFFROOMS mean?
STAFFROOMS noun- A room set aside for the use of staff.