Move window (tab) in tmux
To move a new window to the left do this:
tmux-prefix, :swap-window -t -1
To move window to the right
tmux-prefix, :swap-window -t +1
You can also bind a key to that command:
bind-key S-Left swap-window -t -1
bind-key S-Right swap-window -t +1
Now it will be tmux-prefix, Shift + Left
and tmux-prefix, Shift + Right