What is the ruling on buying a player from one club to another?

The default ruling for engaging in sports is permissibility, as long as it does not involve any impermissible elements such as: exposing 'awrah (private parts), forbidden speech, fanaticism, neglecting obligatory duties, gambling, or harm.

If the sport is free from such impermissible elements, then it is permissible for a club to request its leased player to perform his work in another club, and the first club has the right to receive financial compensation for this, unless there was a prior agreement between the player and the first club not to play for anyone else.