Our understanding of emotion and personality are not comprehensive enough to answer this question in any kind of definitive way, but I am happy to share my thoughts on this topic.
I would say that on some level, there is no relationship between emotion and personality, since all humans experience all the human emotions: love, hate, envy, jealousy, anger, happiness, shame, and so on. It makes no difference what one's personality is. No human being is exempt from these emotions and others.
Some care should be taken to consider what "personality" really is, an area of ongoing research. Is it the Meyers-Briggs constructs of four separate continua in various combinations? Is risk aversion or risk-taking a form of personality? Is personality something we are born with, something that our circumstances create, or something that we construct ourselves?
Assuming that there is some consensus on what personality is and the types there are, there might be relationship between the frequency or magnitude of various emotions, depending on one's personality. For example, a type A personality is likely to experience anger more quickly and strongly than a type B personality. Similarly, a shy personality is likely to experience embarrassment more easily and more deeply than a personality that is outgoing.
But having said all of that, I still maintain we simply do not know enough to answer this question yet, about emotion or personality.