Select the part that you want to delete (click and drag). When selected, press play and check that the selection is correct.
“Edit menu > Remove Audio > Split Delete” to remove the unwanted audio. This will delete the audio and leave a gap where the audio has been deleted.
Click on the “Time Shift Tool” (double headed arrow button <–>) and drag the right hand section a bit further to the right so that you have plenty of space for the new part that you want to insert.
Change back to the normal “selection” tool (short-cut is the F1 key).
Click on the track a little way before you want the new part - this will give you a “lead in” to the new part.
Press the record button. A new track will be formed and start recording.
Record the new part and press Stop (or spacebar) when you are done.
(Optional) Trim off any excess silence from the start/end of the new part.
Change back to the “Time Shift Tool” (short-cut F5 key).
Drag the new clip and the final clip so that the entire sequence plays. It should look something like this: