Select ALL (Ctrl + A), Cut (Ctrl + X), Position playhead at insertion point and Paste (Ctrl +V)
Or just Select All and then drag the whole bunch over with the mouse
From the Premiere Pro manual (I believe track targeting matters, too. That is, the targeted tracks only are copied):
Copy command enhanced to operate on a range in a sequence
The existing Copy command (Edit > Copy, Ctrl+C (Windows), Command+C (Mac OS)) is enhanced when used in the Timeline panel. If there are no clips or keyframes selected, and an In Point or Out Point is set, then the range of time between the In point and Out point is copied to the clipboard.
I just lasso the desired clips and then cut or copy.
...me too ....and I also Shift>Select Clips