What is the expiation for looking at nude pictures and videos of a married female relative online, knowing there is deep regret and a desire to repent?

There is no expiation for this act except sincere repentance. Part of this completeness is to delete and destroy the pictures and videos. The woman must be advised, reminded of Allah, and called to repentance, especially since she is married and has neglected her Lord's command and fallen short in her husband's right, which magnifies the sin. What happened is evidence of the danger of conversations between non-mahrams online, and that they can be a pretext for temptation and evil.