if you replace the front gear system do you need to replace both the rear casette and the rear derailuer or neither I've been given an old bike from the road which has gears where you can't tell what gear the lever is in (there is no number) just a lever in one of three positions or seven for the back).

I am wondering if I upgrade this front gear lever system do I have to upgrade one, both or neither of the (1) rear cassette and (2) rear derailuer?
You can completely change the front setup (shifter, cables, crankset and/or derailleur) completely independently of the cassette and rear derailleur/shifter with no problem. 
If it's a used bike it may be worth checking the chain/cassette are not worn in case the do need to be changed (but would be unrelated to the fact that the front setup was changed)

Update - 
As per comment from @batman, if the size of the crankset has changed the length of the chain may need to be updated also