Are you thinking of using it to feed all the rads on the heating side?, if so, how many rads, including the K3, if you are then you can just use the 2 port valve end contacts to start/stop the exra pump. I can't find any info on that Trident but IMO you might be (far) better off spending a bit extra on a pump like mine, a 6M Wilo Yonos Pico where you can set the pump to CP (constant pressure) control incrementally, in 0.1M steps between 0.5M and 5.5M, which will give you very good control of head pressures etc, you could, if you prefer just go for a simple 3 speed pump settings of say 2M, 4M and 6M, the Wilo also gives this option.
The K3 rad has a rated output of 3.82kw (13.042BTU), to get its full rated output would require flow/return temps of 75C/65C and a flow rate of 5.48LPM but if you are happy enough using flow/return temps of 65C/50C (more efficient running) its output will then be 2.63kw at a 2.51LPM flowrate.
What pump is currently installed and what setting is it on?. what is the boiler flow temperature?. what is the make/model of your boiler.