iCloud
There are new app updates in App Store with old iCloud that I don't have access to the to
iPhone 6s Plus, iOS 9.2.1
If you purchased the apps with a different Apple ID, then you only options are:
1. Go to: Apple - My Apple ID and reset the password on the old ID, so you can enter it to update the apps. It is easiest, when working with two IDs for your purchases, to make the password the same. So, if you are able to make the change, you might want to consider changing it to be the same as your current Apple ID password.
2. If you cannot do that, then you need to delete those apps and re-purchase (or re-download, if free), under your current ID (current ID signed into Settings>iTunes & App Store).
Apps and other media are tied to the Apple ID that they were purchased under.
Cheers,
GB