Your options depend on the type of ticket you have.
Is this one day all by itself on the ticket (i.e. it was only ever a 1-day ticket)? Or was it an unused day from a multi-day ticket?
If it's a partially-used ticket you're stuck with it as-is, and have to use it as a separate ticket.
If it's a Magic Your Way ticket (tickets bought since 2005), they can only be upgraded within 14 days of first use. So even if you bought the No Expiration option, that just keeps the days on the ticket from expiring. After the 14-day window it's locked in to what it was on that date.
If it's a ticket that pre-dates MYW, they stopped upgrading those tickets and locked them as-is.
The only way you'd be able to upgrade an old ticket or apply its value toward a new ticket is if it was a totally-unused ticket. So if it's an unused 1-day ticket, the Lobby Concierge at your hotel *should* be able to apply it toward your new ticket.
But, if it's a MYW ticket and is more than a year old, there's a good reason to wait and do the upgrade at the park... If you visit a park and *use* the ticket to enter the theme park first, and then go to Guest Relations to upgrade, they will give you the current value of the 1-day ticket toward your upgrade. It's a quirk of the WDW ticketing system, but by using the ticket for entry, it "locks" in the current gate price.
Otherwise, there's a chance that you'll only get the value for what you actually paid for the ticket.
(Confused yet?)
-Rob