to take part in a sport or game
to compete against other people or animals in a race
to play against an opponent in a game
to take part in a sport as a member of a particular team, country, etc.
to accept an offer or a challenge (=an offer to fight or compete) that someone has made to you
to have to compete against a person or team
if you enter a race or competition, or if someone enters you, you put your name on the list of those taking part
to take part in a race on a horse, bicycle, motorcycle, etc.