What can I do if my IMEI number has been compromised?

To keep your Apple ID account secure, see the following Apple articles:

Manage and use your Apple ID

Manage and use your Apple ID – Apple Support (UK)

Recognize and avoid phishing messages, phony support calls, and other scams

Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

Identify and filter junk mail in iCloud

Identify and filter junk mail in iCloud - Apple Support

If you think your Apple ID has been compromised

If you think your Apple ID has been compromised - Apple Support

Set up iCloud Keychain

Set up iCloud Keychain - Apple Support

Create a strong password for your Apple ID, It is best if your password consists of eight or more characters and include upper and lowercase letters, and at least one number. You can also add extra characters and punctuation marks to make your password even stronger. 

Never provide your password, passcode, security questions, verification codes, recovery key or any other account security details to anyone else. Apple will never ask you for this information.

See also the following Apple articles:

About the 'Trust This Computer' alert on your iPhone, iPad, or iPod touch

About the 'Trust This Computer' alert on your iPhone, iPad, or iPod touch - Apple Support

Authorize or deauthorize your computer for iTunes Store purchases

Authorize or deauthorize your computer for iTunes Store purchases - Apple Support 

Get a verification code and sign in with two-factor authentication

Get a verification code and sign in with two-factor authentication - Apple Support

Someone might use your IMEI number to clone a jail broken phone but that is not cloning your phone. Don't publish your IMEI and your serial number on any forums and your numbers are safe.

In addition, what Raicya advised about never disclosing your Apple ID and password and phone passcode, your Apple identity and data will be safe.

Thanks for your feedback & you're welcome.

Compromised in what way? It is just an identifier like the serial number.

No