Speed once regulated by local authorities (4)
I believe the answer is:
rate
'speed' is the definition.
(the speed at which something happens)
'regulated by local authorities' is the wordplay.
I cannot quite see how this works, but
'by' could be 'at' and 'at' is located in the answer.
The remaining letters 're' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'once' is the link.
Can you help me to learn more?
(Other definitions for rate that I've seen before include "Tear off, gaining speed" , "See 12" , "The price paid" , "Assess; scold" , "The percentage of a loan charged as interest" .)