Do I need an explicit permission to publish someone else’s table in another paper after citing it?
Unless the paper you are citing it from has been licensed under something like a creative commons license, you most likely need permission.* The good news is, if you're citing from a reputable publisher and publishing with a reputable publisher, this should be easy and free. Below is a screenshot of, as an example, a recently published article from JACS, note the highlighted "Rights and Permissions" link.

Clicking this link will take you to the Copyright Clearance Centre. Follow the on-screen instructions to register your request and receive your license. Most of the major journal publishers and learned societies have a reciprocal agreement that allows content to be reproduced between their journals free of charge.

If an open access article has been licensed under a Creative Commons (or similar) license, you do not need to follow this process, you can just use it under the terms of that license (typically this means that you'd need to include the reference it was taken from and "copyright [year] by [publisher or authors], used under cc-[type]" in the figure caption).

Do be careful with non-commercial use though - if you work in a university, you count as non-commercial, but the publisher probably counts as commercial. So you can't usually rely on a non-commercial permission for republishing in a journal.

*Data itself isn't copyrightable, but the table is. Exactly where the line is drawn (e.g. if you re-typeset a basically identical table) I don't know. But getting permission, in most cases, should be trivial. So there's no reason not to do it.