So I've been told that Zombie Master's effect is that the discard is a cost to activate the effect, and then you proceed to target. This means that you could discard a zombie then summon it directly after the discard.
I've also been told that you need to set a target first, then discard, but this would go against the card text itself:
Once per turn: You can send 1 Monster Card from your hand to the Graveyard, then target 1 Level 4 or lower Zombie-Type monster in either player's Graveyard; Special Summon that target.
I just want to try and verify which one is true, and i cannot find any updated rulings. The only one I was able to find on the subject was from when Upper Deck still had control.