'Private Die' refers to when a customer orders a specific design to be made up. It is usually their family crest and it was a lot more expensive than simply getting the crest engraved.
They are quite uncommon and even rarer is this example which is from Scotland. It was made by Gray and Son in Glasgow in 1833. The crest is probably that of Bartholomew of Glasgow.
This teaspoon is in good condition and is clearly hallmarked. It measures 14.5cm long and weighs 29 grams.