Squeeze ever so slightly on the pliers, whilst pulling gently on the clip you want to remove and it comes out like this:
Some people like to dowse the area with a little boiling water before they do this in order that the plastic is more pliable.
Fitting your new one is simply a reverse procedure of removal. Be cognizant of where the little spring sits before you remove it so you refit it in the correct place.
For any reader who wants to change this little clip on the DC07 cyclone unit, Dyson or new parts suppliers do not sell them. They prefer to sell you a complete cyclone unit. We sell them however, you can get one from us here:
Dyson DC07 Bin Flap Catch. Non UK shipping is no problem, the site will calculate that during checkout.