I have replaced my Alivio rear derailleur with a new Deore M610 but it doesn't shift properly. The casette is a 9 speed Shimano Alivio CS-HG400-9 11-32T and the shifter is an Altus. Do you think this combination would be operating well if set correctly?
The M610 is a 10-speed rear derailleur and is not compatible with 9-speed cassettes and shifters (different pull ratios between 9-speed and 10-speed).
If you want to stay in 9-speeds and Deore, compatible derailleurs are RD-M591 and RD-M592, but they are getting hard to get. You also have other options from other brands.
If you want to keep the derailleur, you'll need a new shifter, cassette and chain. 1-speed deviations are OK for the chainrings and front derailleurs. You can find the compatibility chart here.