Audio-Menu->Advanced->“Detect Silence”. In the following Window you can apply the Changes in Relation to delete the empty Spaces to the Audio-Clip. After that, the previous Audio-Event doesn´t got the empty Spaces anymoe, just the Audio-Signal, which was above the given Threshold.
You can even turn the remain Audio-Clips to a Audio-Part directly, which comes more to your question, when you´ve cut the empty spaces just from scratch. Select the cutted Audio-Events all together and go to Audio-Menu->“Events to Part”. Then you got only the chosen Audio-Events left in an Audio-Part.