Can you set up a new iPhone with your old Apple ID?

The answer to the first part of your question is yes. The second part of the question will involve you removing the pictures from your old iPhone. Back them up to your laptop for example or transfer them someplace else - not to your iCloud account. I've had an Apple ID since 2006 and have had 4 iPhones in that time all set up with the same Apple ID.

jerifrommalawi Said:

"Apple id: Can you set up a new iPhone with your old Apple ID? I want the music and movies but want to start fresh with pictures"

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Apple IDs Cannot be Merged:

I recommend leaving this iPhone associated to the current Apple Account. Elsewise, it is a waste of money on the iPhone.

More on this:

iTunes-purchased Music and Movies are not transferable between Apple IDs, as Apple Accounts cannot be merged. So, if you have made lots of purchases, then you are better off keeping this phone associated to the currently installed Apple ID. But, if these are home music and video files, then all would seem fine between two accounts. So, Prior to the Sign Out...

Back Up the iPhone Before all of this:

Go Here: Back up and restore your iPhone or iPad on Mac or iCloud - Apple Support. That way you can have something to restore it from, should anything go wring with the sign out.