Moving only ahighlighed section on the track?

Ok I do a podcast and each of us hosts have our own track. I have a two second section I want to move up a couple of seconds so what is said isn’t trampled over by the other two tracks. Can I do this? I highlighed the section and selected the move tool but it moves the entire track on the timeline and not just the clip so it will out of sync everything.

How can I do this?

You can move individual audio clips, provided that there is empty space to move them to.
See here about tracks and audio clips:
See here abut the Time Shift tool: