So, it goes Defiant, Defiant, Defiant-A?
More probably Defiant, Defiant, Defiant, Defiant, Defiant-A - we have no reason to think the TOS ship was the first by that name, and even less reason to think there were no Defiants between the TOS ship and the DS9 one.
Of course, the Enterprise-A is something like the twentieth ship by that name at the very least. We have no idea how many starships by that name preceded her, as nothing establishes Archer's ship as the first Enterprise in the starship category. And if Vulcans can have a ship named Intrepid, then there might well have been a million starships named Enterprise in their respective languages before Archer's ship came along...
It's just that with Enterprise, we know for sure that the UFP Starfleet wants to make a sharp distinction between what came before Kirk's ship and what came after. Nothing of the sort is know about any other starship names, such as Defiant.
Timo Saloniemi