You cannot straight away add your new channel to your existing partner program.
You need to apply for it separately.

I remeber when i was filling up the invitation form for joing youtube partner program, it had one of the field to spcify any other channel that we owned. But once we were approved in the program, we could not see that field again anywhere.

Once your new channel also gets approved in the partner prgram, they may give you an option of adding it to the same Adsense account.