When playing with representatives two of them say current player (S'sruuk Héyra (Naalu) and Xxekir Grom (Xxcha)

Who is current player? The speaker or player who plays political card or someone else?

The term "Current Player" is equivalent to "Active Player" which means the player currently taking his/her turn. In this specific case it is the player who played the Assembly SC.

Thx