iMessage to one contact stays on Not Delivered

If it happens to everyone you text, not just them, the problem is your end. Settings > Messages, turn iMessage off and back on, and check Send & Receive has your number ticked. Also make sure the contact is saved with the right number and country code - an old number on the card gives you this too.

If it's only them, the problem is almost always on their side. Phone off, no signal or data, or they've changed number. Another classic is they moved to Android without turning off iMessage, so your iPhone still tries to iMessage a phone that can't receive it. You can long-press the message and send it as a normal text to get it through. If it's been weeks, just ask them some other way whether they switched phones.