Yes (although it's "retarget" more than "recast")
You've quoted the relevant line. It's "a subsequent turn", not "the next turn" or "a subsequent turn as long as its within X amount of time" or anything of the sort. Note that Hunter's Mark requires concentration though, so it's only really an 1 hour if you get hit very infrequently (or not at all) or otherwise get very lucky on your concentration checks (and don't use any other spells that require concentration in the meantime).
Note that you're not "recasting" it in the sense that you're not actually casting a spell when you choose a new target, this matters because for instance this doesn't trigger Mage Slayer attacks and isn't interruptible by Counterspell.