Clearly you need a "Competitor" table if you wish to represent them, which I assume you do! Competitor Name, Age, Sex, Contact etc.
Personally I would create a new table called "Discipline Type" which would differ from "Race Type". The two are functionally independent - race type could be "Triathlon" while "Discipline Type" could be "Swimming"/"Running"/"Road Cycling".
Edit: Sorry, since you wish to include teams, a team will represent a group or a single competitor. Therefore you probably want an "Entry" table which represents a person or Team entering a race Entry would have "Race ID", "Competitor ID" (these two your PK, required), "Team ID", "Team Order", "Team Captain" (binary field, last 3 fields not required). This would then be able to represent individual entries AND team entries. The "Team ID" would link to a "Team" table and would have "Team Name", "Support person contact" etc. Note that the team info is NOT required, so that you can have the same Entry table represent a single entrance from a team or a single entrance from 1 person.