Speed head of police found in bust at quarters (9)
I believe the answer is:
rapidness
'speed' is the definition.
(I've seen this before)
'head of police found in bust at quarters' is the wordplay.
'head of' indicates taking the first letters.
'found in' means one lot of letters goes inside another.
'bust' becomes 'raid' ('raid' can be a synonym of 'bust').
'at quarters' becomes 'ness' (I can't justify this - if you can you should believe this answer much more).
The initial letter of 'police' is 'p'.
'p' going inside 'raid' is 'rapid'.
'rapid'+'ness'='RAPIDNESS'
(Another definition for rapidness that I've seen is " speed".)