If Player A controls Ephara, God of the Polis and casts Hushwing Gryff, will Ephara's draw ability trigger on the next upkeep?

With the “intervening-if” clause, I believe that Ephara's trigger will not happen. Is this the correct interpretation of the interaction?

No, it's not. Ephara's ability will still trigger if Hushwing Gryff is on the battlefield; the Gryff doesn't interfere with Ephara in any way.

Hushwing Gryff stops abilities that trigger when a creature enters the battlefield, but Ephara's triggered ability doesn't do that, because the trigger condition for Ephara's ability is the beginning of an upkeep step, which Hushwing Gryff doesn't care about. The intervening “if” that checks if a creature entered the battlefield during the previous turn is not itself the trigger condition, just an additional check to determine whether or not the ability gets to trigger when its trigger condition occurs.

Daniel Kitachewsky
L4, Paris, France
Rules NetRep