Save game transfer to other/new gamer tag/profile

No,afraid not.Game saves are tied to the account that created them & can not be moved between accounts/profiles.

you should be able to recover you Gamer tag to you new box it will just be you gamer tag not you saved game data you will need a transfer kit or a flash drive for that bit you could also save your GT to a flash drive and move it that way

Previous posting has it spot on

Licence transfer is from console to console, not from game tag to gamer tag, and it is not possible to transfer licences to another profile

There is no way to transfer games save data from one account to another because save data is associated with gamer tag

If you want the gamer tag you can change the Microsoft accounts around. However you will lose all achievements etc from the other account. You'll need to make a new email with Microsoft transfer your old profile to that one then transfer your old email to
the new profile with the desired GamerTag. Otherwise you'll need to change the gamertag on the account with the gamer tag you want then change it to the gamer tag you want on the account you primarily use. Changing your GamerTag costs $10 per switch. So all
and all it'll cost you $20. Good luck my friend.