State Government
(1) Parliament may by law extend or exclude a High Court's jurisdiction to/from a Union territory. (2) Where a State's High Court exercises jurisdiction over a Union territory, the State Legislature cannot alter that jurisdiction, and references to the "Governor" for subordinate-court rules in that territory mean the President instead.
Union Territories generally don't have their own separate High Court - instead, Parliament assigns them to be covered by a neighbouring State's High Court, and importantly, that state's own legislature has no power to change this arrangement since it was set up by Parliament, not the state.
This is why several smaller Union Territories share a High Court with a neighbouring state (for example, Chandigarh being covered by the Punjab and Haryana High Court) rather than each having its own separate High Court.