Do I need to replace 10 speed chain if using a bigger cluster, also 10 speed?
It all depends on how long your chain is currently. Also it depends on if your rear derailleur is a short or mid cage. I would say that a jump up from 24 to 32 is a bit to big for any chain. Of course without seeing how much slack is in your chain right now the right answer will vary. You certainly can put the new cassette on and you will know right away if it work or not. Be warned that you ABSOLUTELY do NOT want to add any more links to your used chain. This is a great resource for drivetrains in general: http://sheldonbrown.com/derailer-adjustment.html#chain