(v2024.7 or higher)
Tap (or click) and hold on a measure (typically the first measure of your selection) and drag. Refine the range by moving the blue selection handles.

Use the menu options:
CUT - the selected area is saved to the clipboard and the space is removed, moving the subsequent measures backwards.
COPY - will save the contents of the selected area to the clipboard.
DELETE - will clear the content of the selected cells without removing space.
INSERT SPACE - will insert empty space (the equivalent length of your selection) pushing the subsequent measures forward.
(External keyboard: use the standard key commands for cut, copy, paste)

PASTE - double tap where you want the measures to paste from, tap Paste. (Moves subsequent measures forward)
External keyboard/mouse: double click a space, Ctrl-V

Paste over - select measures to be deleted (even if it is more than will paste), then Paste. Subsequent measures will place after the pasted measures.

 

 
Older versions
Tap and hold the first bar, then tap on the last space of the last measure you would like to select. Then tap and hold the selected area highlighted in blue.
A menu will appear that will let you choose from Copy, Cut, Delete, Insert space and Cancel Selection.

COPY - will save the content of the selected area to the clipboard.
CUT - the selected area is removed, moving the remaining part of the chord progression back.
DELETE - will clear the content of the selected cells without removing them.
INSERT SPACE - will insert empty space in the length of your selection
CANCEL SELECTION - clear your selection and start over
 
To PASTE it, tap and hold at the location you would like those chords and select:
PASTE INSERT - it will insert those bars
PASTE OVER - it will paste the copied bars from the the selected measure.
CLEAR CLIPBOARD - remove the currently selected bars from your clipboard