On top of difficult circumstances politically and no familial bonds, Gillian has no one who believes in him, especially without ulterior motives, so he can't really open up enough to develop genuine emotional bonds or trust (Asu's not human, after all). So when Sere disinterestedly but completely believes in him, Gillian thinks that she's probably the only person with whom he'll be able to develop such bonds for years, if not his entire life. That's why he wants to ensure that Sere is by his side and tries to have that happen the way which was expected of medieval and early modern royalty: marriage.
Even so, at this point, it's completely platonic. He only begins to show hints in the romantic direction after he finds out that Sere is reincarnated and mentally older, but they're hints and clearly on the emotional side of things, not the physical. They only begin to have romantic involvement after Sere is of age, and physical attraction seems to have come along with them actually having a romantic relationship proper.
More than once, Gillian helps Sere defend herself and the people and places she loves when her own power isn't enough against the OP antagonists. In the end, he encourages Sere to fulfil her dream of travelling the world before trying to marry her. I vaguely recall him not developing into one of those frighteningly possessive male leads, which is both refreshing and necessary for the story, especially given Sere's many important bonds (family, friends, and magic beasts).