The thermostat is the item that you said you wanted to swap over, so that's what I've described for you. To do this, leave the timeswitch wiring alone and make the changes at the thermostat backplane wiring.
1. Black wire presently in the thermostat N is not required isolate it safely.
2. Discard the brown loop of wire
3. The remaining brown wire presently in L at the thermostat goes to 'L / Com' at the new thermostat.
4. The wire presently in terminal 3 goes to 'On / NO' on the new thermostat
5. The earth is not required isolate it safely.
Or..... is the new thermostat actually a programmable thermostat and you also want to remove the old timeswitch as well? If so, 'that's something else altogether.
If you do want to get rid of both, then I reckon my sketch below is how it's wired now. (earths omitted for clarity) But please check to make sure. Terminal 4 isn't shown as being used for anything by the existing programmer, so it appears to have just been used to connect the two grey wires together.
And if the above is correct, this is how it would be after swapping over, with the wiring to the existing thermostat completely removed.