Yes both. clone will get the latest files, and then install will install the files. Including removing the old files, here are the commands you should enter to do a BrickPi3 update on Raspbian:
sudo rm -rf /home/pi/Dexter/BrickPi3
sudo git clone http://www.github.com/DexterInd/BrickPi3.git /home/pi/Dexter/BrickPi3
sudo bash /home/pi/Dexter/BrickPi3/Install/install.sh
After the initial install, reboot is probably not necessary, but it's still advised.