I have a really old iPhone. I no longer have access to the apple account and it does not have cell service. I want to setup for my kids. How can I log out of my old apple account and log in with my current account

Use these steps to remove your personal information from a device --> What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Since you say you do not have access to the old account then that may present a major problem. Apple has two related features, Activation Lock ( Activation Lock for iPhone, iPad, and iPod touch - Apple Support ) and Find My ( iCloud+ - Find My - Apple ), which are designed to prevent anyone else from using an iPhone, iPad, or iPod touch if it's ever lost or stolen. Deactivation of either requires knowing the Apple ID and password that set the feature, or by placing a special request to Apple to reset the device. This Apple ID information essentially defines the current ownership of the device.

Here are additional resources if you are the account owner, or have an Apple accepted proof or purchase:

● Read this article to learn how to remove Activation Lock either on the device itself or on the web --> How to remove Activation Lock - Apple Support

or this one for disabling Find My if activation lock has not yet engaged --> Turn off Find My on your iPhone or other devices - Apple Support

● Help with a lost Apple ID or password:

• For help with a forgotten Apple ID (this is likely an active email address or one used in the past), click here --> If you forgot your Apple ID email address or phone number - Apple Support

• For help with a forgotten Apple ID password, click here --> If you forgot your Apple ID password - Apple Support

● Reset device if you can prove to Apple's satisfaction you are the owner:

Apple can completely reset a device if a person can provide sufficient evidence of valid ownership. This is done online* at: Activation Lock support request - https://al-support.apple.com/#/additional-support Apple says, "Proof of ownership documentation is required," but does not provide many details in the article as to what is acceptable proof. Prior to this official service Apple typically required the original receipt** issued by Apple or an Apple Authorized Reseller and documented provenance (so typically it would be the first owner who does this, or a descendant with legal proof of ownership transfer). Note that while this will let you get use of the device again, it will not help you with lost access to an account.

* There is a special link for this service. You should use it instead of just contacting Apple.

**Apple recommends you keep your receipt after you buy an Apple device. --> Keep your receipt after you buy an Apple device - Apple Support

Re: “… I want to setup [old device] for my kids … with my current account “

While admittedly not answering your immediate question …

… do NOT set up a device w/ your AppleID if children are the intended users.

Avoid the “easy way today” temptation. Setup individual AppleIDs for your kids NOW. (or at least for ONE)

See: Make sure that each family member has a unique Apple ID - Apple Support

Extricating kids from your account “later” becomes exponentially more difficult and painful as time advances.

See:

Set up Family Sharing - Apple Support

Create an Apple ID for your child - Apple Support

Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support