Protect you always
Edgar and Terra's relationship is not a canon relationship in Final Fantasy VI. No, the relationship is strictly fan based. I fell in love with it due to Edgar and Terra being two of my favorite characters in the game. As much as people say that there was nothing going on between Edgar and Terra, I am sure there was something even if it was a little and even if it doesn't seem like a romantical relationship, there was some type of relationship.
When Edgar first meets Terra, she is still unsure about herself. She has no memory on what has happen in her past. Edgar only knows her as the "witch." However, upon first meeting her, he tries his normal tactics of flirting with her since she is a beautiful young woman. However, everything he seems to try fails. At first he thinks he is getting rusty, but that is not true. Terra has no idea what flirting is about or what the emotion love is. However, that doesn't break them apart. Edgar lies to protect her when Kefka stops by his castle. He even lies again causing him, Terra, and Locke to escape his castle upon a daring move leaving his kingdom to submerbed in the desert. This breaks his hidden allegience with Empire causing trouble for his kingdom in the future.
At first, Edgar tries to be different than what the Empire wanted. However, Edgar's ideas are similar. He knows Terra's abilities could help solve the war. This thought doesn't escape Terra's mind and causes her to distant herself from the young king. However, throughout the whole game, Edgar isn't trying to use Terra for her powers. He is trying to understand her and earn her trust. Edgar is always worried about Terra. He wants to make sure that she is safe and free. He wants her to understand who she is, but he also wants to see if she could be a solution to the war that everyone is involved in.
There are no key points regarding Terra and Edgar's relationship. He tries hitting on her at the beginning of the game, but after that, there are no signs. He protects her from Ultros upon the raft, but anybody could have done that. After more characters have join the group, no single person has to place Terra and Edgar together. The relationship is just an idea, but a lovely idea. As I see it, Terra never knew love. Edgar was always rejected or tease. Maybe with Edgar's help, Terra can learn to love someone and Edgar can finally end his flirting with any woman he sees.