There's a couple of things to note here...
Your existing thermostat connects to the boiler through the ebus terminals - it will allow the boiler to run slightly more efficiently and have better control of modulation.
The Hive thermostat may have some clever algorithms, but only has simple on/off control of the boiler - you may lose some efficiency moving to Hive, over a different ebus stat.
You appear to have an Ultimate 2?
To access the wiring connections, you have removed the front panel of the boiler - unfortunately, this forms part of the room sealing of the system; the boiler should be checked over for safety by an RGI, after this seal has been disturbed.
As for the wiring, what model of Hive do you have?
Assuming single channel Hive...
You would remove the wire to the existing stat, from the ebus connector.
You would also remove the red bridging wire from the 24V=RT connector.
Then with a 3 core + earth flex, connect Brown to L
Blue to N
Black to RT
and Green/yellow to earth,
in this connector...
Then, on the Hive backplate...
Brown to L
Blue to N
Black to terminal 3
Green/yellow to earth
And add a short link wire between L and terminal 1.
I hope that makes sense!