You have O(n) in:

a = deque(a)

In order to avoid this, you should use a deque from the beginning like:

from collections import deque

def array_left_rotation(a, n, k):
    a.rotate(-k)

n, k = map(int, input().strip().split(' '))
a = deque(map(int, input().strip().split(' ')))
array_left_rotation(a, n, k);
print(*a, sep=' ')

And array_left_rotation only takes O(k) instead of O(n).

Note that a is pased by reference, so there is no need to return anything, but this could be an issue for some user cases, for this particular problem, it works.