Instructions
Power on the Xbox 360 console and wait for the Dashboard to load. Press the center "Xbox Guide" button on the controller and press "X" to sign out of your Gamertag profile. Turn off the Xbox 360.
Remove the old Xbox 360 hard drive and attach a new one to the console. Turn on the Xbox 360 and wait for the Dashboard to load fully then press the center Xbox Guide button again. Use the analog stick to move the cursor down to the "Recover Gamertag" option then press "A."
A new window will open on the system will instructions for entering your Xbox Live Gamertag email address and password. Use the controller to input your Gamertag credentials then press "A." The console will download or "recover" your Xbox Live Gamertag from Microsoft's servers on to your new Xbox 360 hard drive. You may use the profile on the hard drive once the Gamertag download is complete.