Great question — answering as the UphillTech team:
As @dly said, it depends on the exact competition rules. Some don't allow transferring during the season and some have certain restrictions, such as the UEFA CL. However, I did find some other information as well: According to, funnily enough, @dly on this question, Transfers between clubs are possible during the season, but limited to registration periods. There was a link there, but it led me to a 403 forbidden error, so I'm unsure of its exact contents. I'll provide it anyway. So, basically, in a single national association, a player cannot play for two different clubs in the same matchday unless the transfer is already registered and approved before that matchday.
Full answer by Austin 'AJ' Overton: https://sports.stackexchange.com/a/30364 (CC BY-SA 4.0).
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