A shade carrier (also known as a gimbal or gimble) is used to connect a lampshade with a duplex fitting to a lamp holder. There will be a bit that screws off below the light bulb to hold it in place.  The duplex ring of the lampshade then sits comfortably on top of the shade carrier (but easily removed for cleaning).
This shade carrier will fit a standard 29mm UK bulb holder but has acentral washer that can be removed to fit larger EU 42mm bulb holders.
The size for a shade carrier can be determined by placing your shade on a flat surface and measure from the inner ring down to the flat surface then minus about 2 1/2"/6cm to find the approximate height of the shade carrier that I would recommend.
 
Generally:
For a small/medium table lampshade I would recommend a 4" to 6" gimble
For a large table lamp/small standard lampshade or dome shaped lampshade I would recommend a 6" gimble.
For a larger standard lampshade (tall 18" or 22" shade) Iwould recommend an 8" gimble depending on your base style.