You will need a dual channel version of the Hive to replace it and all of the existing wires are transferred from the terminals of the Honeywell as below....
...to the terminals of the dual channel Hive that have exactly the same functions. So N goes N, L to L, Hot water on, to Hot water on etc...
The Hive doesn't need the links between L, and the 'COM' terminals 5 and 8 that the ST699 has, they are already made internally inside the Hive for you. In your photo the wires would appear to be in the correct terminals as far as I can tell from a photo, when you can't see what is on the other end of them all. HW ON and CH ON are what operate the heating and hot water. [They are just on/off switches]
Unfortunately wiring colours tend to be meaningless with heating systems. One installer may use a blue wire for a certain purpose another may use a brown for the same function. So never assume a blue wire is actually being used as a neutral it may be being used as a live. It's what a wire is connected to at each end that determines its function, not the colour of its insulation.
If there is an existing room thermostat somewhere, that should either be left in situ and set to its maximum setting so that it doesn't interfere with the operation of the Hive, or decommissioned by removing it and making a small modification to the wiring to bridge the switching circuit. If you need any assistance with that, post back details of the existing room thermostat and a photo of its wiring connections.
You don't give any details of the type of heating system this is connected to. So, if your existing system is fully pumped (eg S-Plan or Y-Plan) then you are good to go. If it's an older system with pumped heating and gravity circulation of hot water, then the Hive should be set to gravity mode. The Hive instructions explain how to do this.