I found a project bike that was missing some things and I decided to fix it up. The first image is of the front brake which is missing the piece that clips onto the brake cable. The second image is of the rear brake which has the piece that the front brake needs.
What is this piece called and is it this something I can safely purchase separately or do I get an entirely new assembly ?
I'd probably call it a "brake arm". I'm not that familiar with Tektro brakes but such a significant part isn't generally available as a spare; if it was it would cost almost as much as a new brake. Instead I'd look out for 2nd hand brakes to match (assuming you're not in a hurry). Note that the Novela has had at least one design change, so you might be fitting the whole 2nd hand brake rather than using it for spares. You also need the screw. It might or might not be standard.
It seems to be another BB5 clone. There's some compatibility between brands (I've successfully used a Promax fixed pad adjuster on a BB5) but I wouldn't risk it for the actuator arm.
Your front brake is one of the most safety-critical parts on the bike. I would take no chances.
If it was a bike I wanted to keep using long term, I'd buy the lowest-spec shimano hydraulic brake set (BR-MT200) and replace the whole thing. Search them out, they're plenty good enough and astonishingly cheap for their effectiveness.
If it were a back brake I'd consider substituting a bolt, but a whole arm like that? It's not worth the risk. Save the old caliper and lever as spare parts for the other brake, someday.