Welcome to the Apple Community.
You can't transfer anything you have obtained from iTunes & App stores, but you can transfer your iCloud data (calendars etc) with a little patience.
Whilst you won't lose apps you purchased under the previous account immediately, you will no longer be able to update them. If the previous account was the account belonging to another family member though, you may wish to consider Family Sharing. Family sharing allows you to all have your own accounts but share your purchases. New purchases will be paid for by the organiser unless the individual purchaser has credit on their account from iTunes Store gift vouchers.
You will be given the opportunity to save Safari data, reminders, calendars and contacts to your device as you disable these services in the iCloud settings, which you can later merge with the other account once you login.
You won't be able to save your photo stream photos in the same way, so if you have any photo stream photos that are not already in your camera roll, you should move them there before you delete your account. If you are using iCloud photo library, you must make sure you have saved the original photos to your device before disabling the service.
Your iWork documents can be saved to iTunes on your device, but if you have them on a Mac they would be much easier to save to your desktop there. You can move them back after you switch.
Notes can be shared to messages or mail and copy and pasted back after the switch. Although if you have a Mac, you may find it easier to do there. You could also use a temporary secondary account (see alternative option below) to log into both accounts and copy and paste directly into your other account.
You can set up Mail forwarding at iCloud.com mail preferences (little gear icon-bottom left) to receive mail from your old address to your new one.
As an alternative to just switching, you might consider switching and adding your previous account back as a secondary account at settings > mail, contacts, calendars. You would still need to move your photos and iWork documents and save your safari data, but you'd have access to your old mail, contacts, calendars, reminders and notes.
