When loading an image from an array(image opened with cv2, skimage, etc.) and then saving it in .tif format, the icc_profile is not saved. For example:

import cv2
from PIL import Image, ImageCms

profile = ImageCms.getOpenProfile("AdobeRGB.icm")

img_cv2 = cv2.imread("original.png")
img_pil = Image.fromarray(cv2.cvtColor(img_cv2, cv2.COLOR_BGR2RGB))
img_pil.save("result_cv2_to_pil_tif.tif", icc_profile=profile.tobytes())

However, when doing the same for a ".png" file the icc_profile is saved

img_pil.save("result_cv2_to_pil_tif.tif", icc_profile=profile.tobytes())

I solved it adding the icc_profile to the info attribute prior saving the image:

img_pil.info['icc_profile'] = profile.tobytes()
img_pil.save("result_cv2_to_pil_tif.tif")

It seems a bug in the save method when the file format is .tif, as it not considers adding the icc_profile to the output image if it was not previously in the info attribute.

I haven't tested it with other file formats.