The Black Widow

Veiled Griever is the anonymous character that will first appear in the premiere episode of Season 4: 'A' is for A-l-i-v-e. She visited the funeral of the possible person that was found in Wilden's Police car (specifically the trunk) in the church. She was given the fan-name Veiled Griever because she attended a funeral, and she is probably 'grieving' the loss of someone and she has a veil on.

Posible Identities
Jenna Marshall

It is impossible that the Veiled Griever is Jenna. The huge factor that the Veiled Griever is not Jenna is that Jenna, herself, is standing with the Liars when the Veiled Griever appears.

Melissa Hastings

It may be Melissa because she's possibly in an Alliance with Jenna and Shana, as revealed in the finale of Season 3.

Shana

In the picture above, you can see the skin tone is lighter than Shana's so it can't be her. However, if Shana would wear a mask, it could be her.

Alison DiLaurentis

It could also be Alison as she doesn't want to be seen because she's believed to be dead. So she wears a costume so no one suspects it's her. After all, Alison loves being someone she's not, dressing up, and fooling people. She's a perfect candidate for the identity of the Veiled Griever.