There might be an undocumented method I'm not familiar with (for example, see BoxFrame) but another simple way is to use yyaxis to create two y axes but you'll ignore the right-side axes. Also see this answer to turn off the right axis while keeping visible the other 3 axes.
 It's important the you run yyaxis(ax,'left') after making changes to the right-side so that your plotting is all assigned to the left axes.
 This line links the y limits and ticks for the 2 y axes; otherwise you could remove the tick on the right using ax.YTick = ;
 You may need to call this line again after plotting or hold your axes using hold(ax,'on')