"Waistcoat" here is metonymy for the person wearing the waistcoat. It is parallel to the "boiled shirts" who gather at the graveside in the previous line. (Boiled shirts are well-starched and stiff, like the kind you'd see in Downton Abbey.) Together, the two images present people who are, on the surface, very serious, but don't actually care about the occasion.
The "waistcoat" doesn't seem to be a priest; priests wear robes. He could be an Anglican minister, but it's more likely to single out his collar. It's more likely that he's some grandee of the town, a businessman or rich person. I don't think he's a veteran of the war, or he'd be wearing a uniform.
As to why that person is "leering"... I don't believe it's intended sexually, due to the lack of other sexual references in the poem, but rather in the more general sense of "unpleasant". I suspect that the unpleasantness is more in the way the the objects of the ceremony perceive it, rather than from actual ill intent.
The poem is a series of uncomfortable images of the aftermath of war, and in particular the grief of widows who are being celebrated for their sacrifices. That ceremony feels false. The important people of the city are using it as a way to celebrate their importance: speeches are made, documents are signed, and if you're very lucky, that's all. It would be even worse if they actually thought or spoke about just how awful it is.
I do think that "leering" is an odd choice here: the connotations are inherently sexual. The language hasn't changed that much since the poem was written, and I don't think its connotation is that different in the UK. (Even if it were, the poet is a professor of English, and should be careful about such implications regardless of his own dialect.)
I can only imagine that it's intended to increase the sense of possessiveness and intrusion: this puffed-up poo-bah is using their grief as a prop. Perhaps I'm oversensitive to shy away from the sexual connotations, a bit like using "rape" for something merely unpleasant.
