[bash] What command means "do nothing" in a conditional in Bash?

You can probably just use the true command:

if [ "$a" -ge 10 ]; then
    true
elif [ "$a" -le 5 ]; then
    echo "1"
else
    echo "2"
fi

An alternative, in your example case (but not necessarily everywhere) is to re-order your if/else:

if [ "$a" -le 5 ]; then
    echo "1"
elif [ "$a" -lt 10 ]; then
    echo "2"
fi