Anyone can be afraid of competition, but it may be more obvious in characters with certain aptitudes, such as athletes, politicians, and businesspeople. A fear of competition is almost always rooted in a fear of failure, making a certain amount of trepidation or worry in this area normal. But it becomes a problem when it tanks the character's self-esteem, discourages them from pursuing their dreams, or causes them to abandon their ethics to neutralize the threat. As with many fears, this can manifest one of two ways for the character: avoidance of competition altogether, or going to any length to neutralize competitors (thereby ensuring success).

Being intrinsically rather than extrinsically motivated (the character choosing to compete against themselves instead of other people)
Being a peacekeeper
Being highly sensitive to criticism
Opting to watch games instead of participating in them
Avoiding competitive board and card games
Being uncomfortable around people who talk trash and play mind games during recreational activities
The character downplaying an area of giftedness so no one will ask them to perform in that area
Settling into their career; not attempting to climb the corporate ladder
Procrastinating
Taking background roles; staying out of the spotlight
Choosing hobbies and pursuing passions that are non-competitive in nature
Rapidly losing interest in something when someone else outstrips the character's performance
Not wanting to invite others to join an activity or hobby in fear they'll take it over
Seeing talented co-workers, classmates, and teammates as threats, not allies
An inability to learn from others
Reveling in other people's praise or recognition