Among all of Quark's employees, the waiter is on the bottom rung. However, it seems Quark relies on Broik more than other the other Ferengi waiters. Ferengi costumes such as this one can be seen in most episodes of Deep Space Nine, such as 'The Emissary' and 'Favor The Bold'.
David Levinson portrayed Broik an impressive 68 times, and even though virtually never spoke, he was commonly seen and referred to. This particular Ferengi waiter costume is likely an early one as it is a bit worn from use, and a friend of mine also owns an identical Broik that is in markedly better condition.