If I Update New Plugin old functions will work?

This solely depends on which function you use. Removed function will not work anymore. You will have to analyse that in the exiting code.

so If I used old plugin functions, do I need to update with alternate approach ?

What alternate approach do you mean?

for example In my current version I am using "isusersystemadministrator" function , if I update with new version is my rule will throw error or It will work ? because in new version list this function is not listed.

If that new version does not provide this function anymore, your expression will stop working.

I am not sure new version will have old functions and having additional features or only having new features ?

want to confirm this !

I don't know. You will have to try it.

In terms of long term maintainability, there is no way around keeping your plugins updated. And if a function is removed, you will have to update your app.

Unknown said:

below are the difference between old and new functions list 

you are mistaken here, i believe.  the "key features and functionality" list from the plug-in's description page is **NOT** an all-inclusive list of all functions the plug-in will contain, it is merely a passive description.  I can almost guarantee you that nearly all of the current functions will still be in the updated version (some may have been removed and some may have been replaced with iterated versions - the documentation on this is often very unclear unfortunately).

Thanks for the confirmation.

It is generic concept of code versioning. Whatever is present in latest version will work, if some features are removed from latest version it won't work.