His character could become more closed - off. Losing Peter, who was such an important part of his life, might make Yondu build higher walls around himself to avoid getting hurt again.
I like the fanfiction 'The Redemption of Yondu'. It shows Yondu's journey towards redemption and how Peter plays a part in it. It's a story that gives more depth to Yondu's character. Another is 'Peter's Discovery'. Here, Peter discovers something about his past that was related to Yondu and it changes their relationship in a new way. Also, 'Yondu and Peter: A New Beginning' is a fanfiction that starts a new adventure for them, with a fresh perspective on their bond.