One of my contacts has recently switched to an iPhone. How can I tell my phone to send them iMessages now?
It ought to figure it out for itself, once their phone is set up correctly.
So long as their phone number is listed in their phone, in Settings > Messages > Send & Receive as "You can be reached by iMessages at..." then it should just switch over.
You'll see their messages start to appear in blue rather than green.
You can test/check by finding them in Contacts. As you open their details, you should see FaceTime light up, which confirms they're on an iPhone.