No one will be able to help from that photograph unfortunately.
Apart from not being able to see where all of the wires are actually connected, we would need to know what is at the other end of them to advise you. The colours don't help, because they would have been chosen according to the personal preferences of the installer and the available cables used to install it.
It would be a bit like dropping you at an unknown busy intersection of roads without any road signs and asking you to identify the roads to London, to Liverpool, to Largs and to Llandudno. And in this case, there are only 4 of them to get right!
Your existing room thermostat should be decommissioned to prevent it interfering with the operation of the Hive. It cannot simply be disconnected, otherwise the heating control wiring will be 'open circuit' and the heating will never come on. This means that the existing thermostat switching wires will need to be bridged out by connecting them together at some convenient point.
Simply turning the existing room thermostat up to maximum and leaving them there, will achieve the same thing, but there is always the danger that it could be inadvertently turned down.
If you need any further assistance, please post a photograph of the existing thermostat showing the wiring connected to its terminals and stating its make & model. Someone should then be able to work out what each wire does from that and provide further assistance.
Your use of the word Thermostats (plural) puzzles me a little, unless you have multiple heating zones in your home. If one of the thermostats you are referring to is a hot water cylinder thermostat, that stays as it is. The Hive only provides on/off control for the hot water.
