In the Antarctic Late Summer Update, Professional Army's effect of providing a resource discount on unit upgrades was transferred to Retinues and its original effects were inherited by Force Modernization.
This is one of the most useful Military Policies in the entire game, hands down! The process of upgrading your military units is constant, going throughout the entire game. All upgrades cost Gold, and after the Medieval Era they start costing quite a bit of it! It goes without saying how valuable Professional Army is for cutting these costs in half, especially when the normal cost of upgrading units is 300+ Gold!
The way to use this Policy is: you gather your Gold (using other permanent Gold-saving Policies in the meantime, such as Conscription), you develop your tech, and when you're ready you slot Professional Army and upgrade as many units as you can for the several turns you will have the Policy. Then slot back the money-saving Policy. Rinse and repeat as necessary. For militaristic civilizations with lots of units this is especially useful, as they will spend huge amounts of Gold both to maintain their army and to upgrade it - any savings are very welcome!
Of course, sometimes there will be emergencies, such as when a neighbor declares a Surprise War and you find yourself with an outdated army. In such cases you might want to upgrade several crucial units right away, without waiting to slot Professional Army.
In the early medieval period, serfs and villeins formed the bulk of the armies; barely trained and ill-equipped, other than sheer numbers, they were pretty useless in battle. The idea of a state-maintained “professional” army had faded – as so much else did – with the Roman Empire (although China still had one). But as various nations coalesced out of the ruins, kings began to supplement their mobs drawn from feudal lords with paid professionals. These soldiers were usually housed in barracks and segregated from the civilian population to minimize friction, and the king provided their food, weapons, clothes, and training. They were (almost) always more effective than the amateurs.