"serious personality" is correct and usable in written English.
You could use it to refer to someone who has a character trait of being earnest and no-nonsense. For example, "She has a serious personality that makes her well-suited for her role as a manager."
Mr. Wang is the serious personality, almost professorial in demeanor.
Have you ever had a serious personality clash with your manager or work colleagues?
Eden is a musical prodigy on the cusp of a serious personality disorder that Iris fears could be dangerous.
"It has traditionally required a serious mental illness such as psychosis or serious personality disorder to prove insanity.
One of my most serious personality flaws is a tendency to speak critically before thinking about the potential impact on others.
The serious personality disorder which affected Steven flickered into his parents' consciousness when he became gripped by paranoia at the age of 10.
Dangerous and severe personality disorder is a controversial working definition for a small group of people posing a significant risk of very serious harm to others.
Current research and policy from the Ministry of Justice, the Department of Health, and the National Institute for Health and Care Excellence (Nice) on the detention of serious offenders suffering from severe personality disorders indicate that they should be detained in prison rather than in hospital.
Andrea Williams showed that Brian Williams isn't the only serious NBC News personality willing to cut loose with the cast of "30 Rock".
The indication for use of medication usually differs between patients with serious depression, personality disorders or crisis reactions.
Severe borderline personality disorder is a serious psychological disorder that is associated with high burden.
