Qualify tracks in Career mode are unlocked one at a time. In order to unlock the next Qualify track you must get 3rd place or better on the current track. The better the placement the more silver coins and rep you will earn, but you’re only required to get 3rd place to progress to the next track.
If you’re having trouble beating a track we suggest you upgrade your current bike or buy the next bike. Sometimes you might be losing because you are not taking the correct line. Try to find alternative lines (or watch what lines your opponents take) and see if those lines are faster.