It's not possible with starmap(), but it's possible with a patch adding Pool.istarmap(). It's based on the code for imap(). All you have to do, is create the istarmap.py-file and import the module to apply the patch before you make your regular multiprocessing-imports.

Python <3.8

# istarmap.py for Python <3.8
import multiprocessing.pool as mpp


def istarmap(self, func, iterable, chunksize=1):
    """starmap-version of imap
    """
    if self._state != mpp.RUN:
        raise ValueError("Pool not running")

    if chunksize < 1:
        raise ValueError(
            "Chunksize must be 1+, not {0:n}".format(
                chunksize))

    task_batches = mpp.Pool._get_tasks(func, iterable, chunksize)
    result = mpp.IMapIterator(self._cache)
    self._taskqueue.put(
        (
            self._guarded_task_generation(result._job,
                                          mpp.starmapstar,
                                          task_batches),
            result._set_length
        ))
    return (item for chunk in result for item in chunk)


mpp.Pool.istarmap = istarmap

Python 3.8+

# istarmap.py for Python 3.8+
import multiprocessing.pool as mpp


def istarmap(self, func, iterable, chunksize=1):
    """starmap-version of imap
    """
    self._check_running()
    if chunksize < 1:
        raise ValueError(
            "Chunksize must be 1+, not {0:n}".format(
                chunksize))

    task_batches = mpp.Pool._get_tasks(func, iterable, chunksize)
    result = mpp.IMapIterator(self)
    self._taskqueue.put(
        (
            self._guarded_task_generation(result._job,
                                          mpp.starmapstar,
                                          task_batches),
            result._set_length
        ))
    return (item for chunk in result for item in chunk)


mpp.Pool.istarmap = istarmap

Then in your script:

import istarmap  # import to apply patch
from multiprocessing import Pool
import tqdm    


def foo(a, b):
    for _ in range(int(50e6)):
        pass
    return a, b    


if __name__ == '__main__':

    with Pool(4) as pool:
        iterable = [(i, 'x') for i in range(10)]
        for _ in tqdm.tqdm(pool.istarmap(foo, iterable),
                           total=len(iterable)):
            pass

The simplest way would probably be to apply tqdm() around the inputs, rather than the mapping function. For example:

inputs = zip(param1, param2, param3)
with mp.Pool(8) as pool:
    results = pool.starmap(my_function, tqdm.tqdm(inputs, total=len(param1)))