At the end of Carrer de Quart, the continuation of Carrer dels Cavallers, you’ll find the Porta de Quart, one of only two remaining gates to the old town.
Guarding the approach from the river, on the north east side of El Carme, is the more impressive Porta de Serranos. You can pay to go up the towers to get a view.
I’ve made a separate post about Eating in El Carme. My map with everything on is here.
See also my separate post on Street Art in El Carme for other things to see in the barrio.