From http://rhnh.net/2014/04/26/bash-script-to-keep-a-git-clone-synced-with-a-remote

app_update.sh

function update_git_repo() {
  GIT_DIR=$1
  GIT_REMOTE=$2
  GIT_BRANCH=${3:-master}

  if [ ! -d $GIT_DIR ]; then
    CURRENT_SHA=""
    git clone --depth 1 $GIT_REMOTE $GIT_DIR -b $GIT_BRANCH
  else
    CURRENT_REMOTE=$(cd $GIT_DIR && git config --get remote.origin.url || true)

    if [ "$GIT_REMOTE" == "$CURRENT_REMOTE" ]; then
      CURRENT_SHA=$(cat $GIT_DIR/.git/refs/heads/$GIT_BRANCH)
    else
      rm -Rf $GIT_DIR
      exit 0 # Process manager should restart this script
    fi
  fi

  cd $GIT_DIR && \
    git fetch && \
    git reset --hard origin/$GIT_BRANCH

  NEW_SHA=$(cat $GIT_DIR/.git/refs/heads/$GIT_BRANCH)
}

update_git_repo "/tmp/myrepo" "git://example.com/my/repo.git"

sleep 60 # No need for a tight loop