Green’s Dictionary of Slang

1. a person who snacks.

1999

Guardian G2 25 June 6: Grazers, browsers, solitary munchers [...] that’s what we are these days.

2. (UK Und.) a tramp who rifles through rubbish bins for food.

1990

J. Healy Streets Above Us (1991) 2: The only sound the leisurely shuffle of the experienced grazer as he goes from bin to bin.