How do sync my iPhone to a new itunes without having it be deleted?

How do sync my iPhone to a new itunes without having it be deleted?

May be, it will not be possible. But what you can do is:
(1) Import your music and video library to iTunes.
(2)Connect your iPhone to PC & it will be detected in iTunes.
(3)Backup your iPhone to iTunes so it will back up all your purchases. (all purchased music, videos, app and movies)

you will have your data to be deleted if you want to sync with new iTunes.

(4)Then restore your phone so all app data and purchases will be restored.
(5)And then sync music, videos, photo you have imported.

An iPhone can be synced with only one iTunes account at a time. Once you switched iPhone to a new iTunes account or a new computer. You have to authorize the iPhone to it in advanced, then you can upload music and video from the new iTunes to your iPhone. But this way will overwrite the original files on iPhone with the new iTunes library. You may try this iPhone fiel manager, it can help you copy files from iPhone to computer for backup, you can also use it as an iTunes alternative to upload songs, photos and videos. It will not erase your original iPhone files. It's safe and works pretty well for me.