So according to Webster below me, staggard is a term for "the male red deer when four years old". The word itself is etymologically simple, stag, n. + your generic -ard suffix.
OK, right, but why is there a word for this? What's so special about a four-year-old male red deer that it needs its own name?
For one, these were animals one hunted. Hunting, for the English aristocracy, is and always has been a tremendously big to-do. When you regaled the court with your exploits, you wanted to be able to telegraph exactly how impressive your prize was. Let's take a line from George Gascoigne's 1575 Noble Arte Venerie: An Hart is called the firste yeare a Calfe, the seconde a Brocket, the thirde a Spayde, the fourth a Staggerd, the fifth a Stagge. So it's little like high school, where you have Freshmen, Sophomores, Juniors and Seniors, though perhaps not for the killing.
The Pokémon evolution chain of the male Cervus elaphus
||This one makes sense!
||From the French for broach, in the sense of a tapering pointed
instrument or object. This is the year where a deer gets its first
horns, which, appropriately, are "straight and single, like a small
dagger" (OED). This is just a red deer word - if it's a fallow deer,
they're called prickets (heh).
||Spaya(r)d, or spayd
||According to the OED, the origin for this one is obscure. User Glowing Fish wonders if it might not derive from the shape of a spade, since the antlers are broadening at this stage. User Clockmaker seconds the suggestion: "I wonder if the »spayd« is called that because it develops the cup of
the horn that year, or something; I don't know if it does do that, but
it would be symmetrical with »brocket«, and in Swedish the cup of the
antler is called a »shovel«, so... »spade«."
||See above! Stag, n. + -ard.
||This is a word we use today!
||A male red deer at its prime! Harts of the species were the most prestigious Medieval game.
misterfuffie says re Staggard: It's also not uncommon even today for landowners who hunt to be familiar with individual deer from year to year - I would imagine the familiarity would have been even greater when you were an idle noble with nothing to do but hunt. So it's entirely possible that they'd have known how old the buck was based on knowing it from birth.
Love and thanks, Oxford English Dictionary!