you will need a live and neutral to power the Hive hub (usually fitted next to the boiler but doesnt have to be) then the two wires from your existing thermostat are wired into the hub too, if you havent opened your Hive and can send it back, then go for Nest E this is battery powered and would just use the two wires that your existing thermostat uses
The Hive receiver replaces your programmer, if you have one.
The old thermostat wires are not required, as the Hive thermostat is battery powered. However, the 2 wires must be joined to form a full circuit, else your heating will not work. OR the wires need to be disconnected from your junction box, and the circuit completed there.
OP the comments made so far may appear contradictory, and the reason for that is that you don't give enough information, so assumptions are made.
If you have a combi boiler, the Hive (Single Channel Version) is generally wired direct to the boiler as there is no requirement for time control of the domestic hot water. The water is heated instantaneously when a hot tap is opened.
If you have a system with a hot water cylinder that requires timed control for heating the hot water, then the Hive (Dual Channel Version) replaces the existing programmer / timeswitch. How, will vary depending for example whether you have a system with 2-Port motorised valves / a 3 -Port motorised valve / pumped only central heating / etc.,
The bottom line is, you need to provide more information for a definitive answer.
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