Your existing stat is battery operated.
The regular Nest Heatlink requires a Live and Neutral to operate.
Assuming that your boiler is mains switching; its possible that the grey wire hiding behind the Timeguard can be used for this purpose, but you will need to ensure it is connected to a neutral at its other end.
However, it's common to install the Heatlink next to the boiler, the existing wiring to the Timeguard can then be utilised to power the Nest Thermostat with 12v (via connections T1 and T2 on the Heatlink), as long as the Timeguard was mounted in a convenient location.
Alternatively, and very simply, the battery operated Heatlink of the Nest Thermostat E, could directly replace the Timeguard in place.
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