Q: how to add a new device to my apple account

The following has instructions on how she can remove her information: What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support

Once that is done you can set it up as if it was new and it will have you log in to your account.

Hi

Go to settings on iPhone find my iphone turn this off

Then settings restore iPhone to factory settings.

Then iphone is ready for new user .

Cheers

Brian

Hi

Then se up iPhone with your apple ID set up as new or when it asks  use iCloud back up from your other device

If you have one.

Cheers

Brian

It is best to restore it to Factory settings as has been recommended, but it is not absolutely required. You want to make sure that your ID is signed in in the following places:

Settings>iTunes & App Store

Settings>iCloud

Settings>FaceTime

Settings>Messages

If you decide not to restore to Factory settings, then be aware that any apps on the device that need to be updated will ask for your Wife's Apple ID password when you update them.

Also, when you sign into a new iCloud account, the Notes, Calendars, Photo Stream from your Wife's iCloud account will be removed, and yours will replace them. For Contacts, if you wish to merge the contacts that are on the current device, when you sign your Wife's ID out of iCloud, you would elect to "Keep" the Contacts, and then when you sign in your iCloud ID, you would elect to "Merge" them with your iCloud account.

Photo Stream Photos can be selected and put into a Shared Album that you send to yourself if you want to preserve those.

Best of luck,

GB