North Sindarin is an extinct dialect of Sindarin.
The Sindar of Beleriand were divided in several groups, and their language had developed some dialects. North Sindarin, the flavour of Sindarin spoken by the Mithrim, the northernmost group of the Sindar, differed from the Sindarin of Beleriand proper in many aspects. It was this language which was adopted by the exiled Noldor after their return to Middle-earth, and by their mortal allies. During this time North Sindarin was changed much, partially due to the adoption of Quenya features, and partially due to the love of the Noldor for making linguistic changes. Beren's heritage was clear to Thingol of Doriath as he spoke the North Sindarin of his homeland.
North Sindarin retained many features of Archaic Sindarin which had been lost in the Sindarin of Beleriand proper, but also went through several changes of its own: lenition occurred far less in this dialect than in the other dialects.
After the end of the First Age, the survivors of Beleriand's realms generally adopted the more southern variants of Sindarin, but several proper names which are uninterpretable in normal Sindarin which remained in use during the Third Age show North Sindarin influence.