When studying personality traits, we're usually talking about five really important ones (a.k.a. "The Big Five"): openness to new experiences, conscientiousness, extraversion, agreeableness, and neuroticism. Unlike the Myers-Briggs type of personality test, tests analyzing these characteristics give everyone a score somewhere on the spectrum of these traits. So, we all end up being some level of agreeable, conscientious, and so forth.
These traits are thought to be somewhat innate: Previous research has suggested that a large chunk of them — about half — is inherited genetically. But, this line of research necessarily ignores many other factors in our family environment. So, even if we inherit a lot, that doesn't necessarily mean we're doomed to live a life of being more or less neurotic. And, we already know it's possible to change our levels of these traits over time because they often fluctuate naturally throughout our lives.
However, if we're talking major shifts in personality, there might be an age cutoff. Other work has suggested that we become less open to new experiences as well as more neurotic and introverted between ages 18 and 30. This is not exactly a good recipe for being open to change. And, indeed, one study shows our traits tend to settle down and solidify after 30. Here, the trend showed up regardless of sex, education, and ethnicity. But, other research suggests that changes in our personalities tend to come with big life moments, so they can change at any age when those moment happen.
So, can we change ourselves and our lives after 30? Absolutely. But, that doesn't mean it will be easy, and it'll just get more difficult the more we become stuck in our ways. Which means that, if you want to change, you should probably get the major transformations out of the way ASAP. Otherwise, you could just focus your efforts on whichever traits matter most to you.