The Hyperion-class cruisers were the first Starfleet vessels to carry subspace radio transceivers. They were in service beginning in 2194. (The Starfleet Museum)

Prior to the development of the transtator in 2185, only specialized communications ships were powerful enough for the large arrays needed to transmit subspace signals.

This is consistent with TOS: "A Piece of the Action", where it is recounted that Horizon didn't have subspace communications capabilities in the 2160s. But it is inconsistent with Star Trek: Enterprise, where the NX-01 did have those capabilities.
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