Police force raised detective's rates (5)
I believe the answer is:
tempi
'rates' is the definition.
(tempo is a kind of rate)
'police force raised detective's' is the wordplay.
'police force' becomes 'met' (short for Metropolitan Police Service).
'raised' is a reversal indicator (going up in a down clue).
'detective' becomes 'pi' (private investigator).
'met' reversed gives 'tem'.
'tem'+'pi'='TEMPI'
(Other definitions for tempi that I've seen before include "Times" , "Speeds, rhythms of musical pieces" , "Rates" , "Speeds (music)" , "Beats" .)