A thief has a “hear noise” ability, but the cleric has functional ears too, and the thief is busy having been flattened by the falling stone trap. Also, the cleric only knows animate dead, not raise dead. How does she listen for the snoring dragon behind that door?
All characters have a percentage chance to hear noises.
There is long section of rule text in the 1e DMG (pg 60, Efreet cover, Door to Heck cover) — but it consistently refers to "characters" listening, with no special call out to the thief class or any other class. A generous reading is that any person could listen with the same chance as a 1st level thief.
In AD&D 2nd Edition DMG (pg 129 Dragon Wizard cover, pg 175 Humanoids cover) there is this (plus more), which makes that reading explicit.
All characters have a percentage chance to hear noises, the percentage varying by race, as listed on Table 83. This ability is equal to that of a 1st-level thief (however, thieves can choose to increase this score).
So .. the cleric can listen at the door like anyone else.
It's up to you
In A Quick Primer for Old School Gaming, Matthew J. Finch describes how players used to play without ability checks. (Emphasis mine)
"The players can describe any action, without needing to look at a character sheet to see if they ‘can’ do it. The GM, in turn, uses common sense to decide what happens."
"You don’t have a ‘spot’ check to let you notice hidden traps and levers, you don’t have a ‘bluff’ check to let you automatically fool a suspicious city guardsman [...]"
As you can see for yourself, there is no "check". The character simply tells you he listens closely and you determine whether he can hear the snoring dragon or not.
You can read more about skill checks here.