Kate debuted these earrings at Royal Ascot 2016.
Here is the closeup:
They are pear-shaped diamond drops framed by smaller white diamonds in what I believe is a white gold setting. Suspended from the diamond is a diamond-encrusted cap on top of a freshwater white pearl.
Anna of My Small Obsessions believes this to be a bespoke design from Robinson Pelham.
Robinson Pelham declined to confirm if these are their designs. I personally agree with Anna, They look too similar to already-made designs from RP to not be from that company.
Since we are only making educated guesses and have no real confirmation from RP, I will not label these as their creations until I receive firm words from the company.
Here they are on Kate.