Regulator into lowering current a little in Missouri River (7)
I believe the answer is:
monitor
'regulator' is the definition.
(monitor is a kind of regulator)
'little in missouri river' is the wordplay.
'little' becomes 'onit' (I can't justify this - if you can you should give a lot more credence to this answer).
'in' means one lot of letters goes inside another.
'missouri' becomes 'mo'.
'river' becomes 'r' (abbreviation for river).
'onit' inserted into 'mo' is 'monito'.
'monito'+'r'='MONITOR'
'into lowering current a' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
(Other definitions for monitor that I've seen before include "Prefect; a loudspeaker" , "what a computer user may require" , "Watch - lizard - warship - VDU" , "Supervise" , "Keep a watching brief" .)