Hi
The indicated part on your carb is the choke pull off, which dampens the opening of the secondary air valve as well as cracking open the choke when the engine first starts. I'm guessing this car doesn't start well when cold.
Once the engine is warmed up the choke pull off won't affect the running of the engine except under hard acceleration. If the car dies while driving there is a good chance that the choke is closing. In your picture I can see that you have an original choke thermostat - the new ones have a slightly different connector. Chances are that the electric choke isn't working causing the choke to stay closed or to only open a bit when driving, which will stall the engine.
So, you've probably got 2 issues - a bad choke pull off and a bad choke, both of which should be fixed with a rebuilt carb.
You will want to make sure that there is power to the choke when the engine is running. The choke is wired through the oil pressure switch so a bad switch will cause the choke not to work.
Hope that helps!