There are two issues with your code.
- the number you obtain with list.pop() is not the one you just checked with your condition (it is merely the last one in the list)
- When you reach 3, list.pop() removes 6,
- When you reach 4, list.pop() removes 5,
- You never reach 5 because you're at the end of what remains of the list at that point.
- removing items from a list within a for-loop on the same list will cause the for-loop to skip items or complain that the list changed during iterations. So, even if you were to pop the appropriate number, your loop would miss items.
You also don't need to sort new_list every time you add to it, you can do it once at the end, but that just optimization.
Instead of a for-loop, you could use the sort method with a key parameter that returns a boolean indicating True for elements that do not meet your conditions (i.e that will be shifted to the right). Because Python's sort is stable, this will only place elements in two groups without otherwise changing their relative order.
L = [0, 2, 4, 6, 1, 3, 5]
L.sort(key=lambda x: not x>=3)
print(L) # [4, 6, 3, 5, 0, 2, 1]
If you need a more procedural solution, you can separate the values in two lists that you stick together at the end:
L = [0, 2, 4, 6, 1, 3, 5]
left,right = [], []
for x in L:
if x >= 3: left.append(x)
else: right.append(x)
L = left + right
# [4, 6, 3, 5, 0, 2, 1]