- To establish Do Not Disturb for a chat thread, open the Messages app and touch on it.
- On the upper right, tap the blue circle with an 'i.'
- To enable the Do Not Disturb option for this contact, move the Hide Alerts slider to the right.
- Don't forget to tap Done.
Unless you turn off the Hide Alerts option, you should no longer get any notifications from this person. Alternatively, you may achieve the same thing by swiping left on the discussion thread in Messages and selecting Show Alerts.