How do I link my Apple ID from my phone to my iPad, which is currently showing an old work e-mail address

You must maintain your AppleID account - keeping your email address (used to identify and sign-in to your AppleID account) up-to-date as it will inevitably change over time.

While your AppleID account is intended to be used for life, your purchased Apps and subscribed services are forever associated with the AppleID account from which they were purchased, few of us will keep the same email address forever. Your email address is easily changed from your account.

If your AppleID credential have been forgotten, they can be recovered here:

https://iforgot.apple.com

To recover your credentials, you’ll need access to one of the following:

• Your primary email address mailbox that corresponds with your AppleID
• Any of the secondary/recovery email addresses that should be configured for your AppleID account
• Any of the trusted telephone numbers (fixed line or Cellular/Mobile) that are associated with your AppleID

Unless you AppleID account has not been fully/correctly configured, or has been seriously neglected, recovery of the AppleID and password should not be difficult.

More information about recovery of your AppleID:

If you forgot your Apple ID - Apple Support

More information about recovery of your AppleID password:

If you forgot your Apple ID password - Apple Support

When you recover access to your credentials, you would be well advised to log-in to your AppleID account from a web browser - and verify/update any email addresses and trusted telephone numbers:

https://appleid.apple.com

Are you suggesting that your iPad and iPhone use different AppleIDs? If so, to “link” (i.e., synchronise) via iCloud, you’ll need to sign-in to both with the same AppleID account credentials.