Laser-induced spin transport is a key ingredient in ultrafast spin dynamics. However, it remains debated to what extent ultrafast magnetization dynamics generates spin currents and vice versa. We use time- and spin-resolved photoemission spectroscopy to study an antiferromagnetically coupled Gd/Fe bilayer, a prototype system for all-optical switching. Spin transport leads to an ultrafast drop of the spin polarization at the Gd surface, demonstrating angular-momentum transfer over several nanometers. Thereby, Fe acts as spin filter, absorbing spin majority but reflecting spin minority electrons. Spin transport from Gd to Fe was corroborated by an ultrafast increase of the Fe spin polarization in a reversed Fe/Gd bilayer. In contrast, for a pure Gd film, spin transport into the tungsten substrate can be neglected, as spin polarization stays constant. Our results suggest that ultrafast spin transport drives the magnetization dynamics in Gd/Fe and reveal microscopic insights into ultrafast spin dynamics.