It's a kilt pin, that used to belong to my mother's maternal grandfather (who died before she was born).
We were always told it was an eagle's talon, but it never looked all that vicious to me. I did a bit of searching online, and it seems it's more likely a grouse's claw. These kilt pins were manufactured in the 1910s and usually have a gem on the ring in the middle, plus another gem at the end of the metal. It's an interesting object, but you can buy complete ones for £25 on eBay.
The stag (which, as with anything my mum owned that had something accidentally-snap-offable has a piece snapped off) is normally the other way up on these pins. They're meant to be worn with the claw pointing up, but this one was made (or perhaps adapted) to be worn with the claw pointing down. I don't expect this to make it a desirable collectible.
I think I'll hang onto it in case one of her relatives wants it, but given that its original owner died in 1936 I don't think there will be many people around who will have a sentimental attraction to it.