Once you've purchased a track, it needs to be downloaded to your computer or phone. Then you can play it as many times as you want.
You can download using a desktop computer or on mobile, except perhaps some older iPhones which don't permit downloading of files.
Or follow this link: https://www.beatport.com/library
On mobile, tap the 3 dots to the right of the track:
If you haven't yet downloaded the track you should see a tick like this:
If you've already downloaded it, you'll see a blue download icon like below. You need to click this icon.
This where you can download the track by clicking the blue download icon: