To Solve Sumaq’s murder in investigate Sumaq’s murder in the Hidden City in Shadow of the Tomb Raider talk to the musician down stairs to get the crowd to disperse.
Once inside be sure to talk to the 6 people down and upstairs until you no longer enter cutscenes by talking to them. Also examine the body. Walk past the lady in the back area and around the back of the house.
Climb around until you get into the servant’s room. Examine any further evidence. Then go back out the house and turn left. Dig in the earth until you find a knife. Go back to the guard and inform him of your findings.