Agree with the above.
Most garden variety HTN can be managed by internists and family doc types, and it is.
For really badass HTN unresponsive to multiple meds, or otherwise atypical, the "HTN specialist" docs (or special HTN clinic, which we had @ the med center where I did residency) may be run either by cardiologists or nephrologists. It seems like nephrology more often, but @my hospital it was basically run by a couple of cardiologists (the noninterventional types).