If blink counts as teleporting then an opportunity attack is not provoked
The Polearm Master feat states:
[...] other creatures provoke an opportunity attack from you when they enter your reach.
Note that this is just a regular opportunity attack, there is nothing special about it besides when it is provoked so it follow all the usual rules on opportunity attacks including this:
[...] You also don't provoke an opportunity attack when you teleport [...]
If Polearm Master worked against teleporting targets it would have to make an explicit exception to the general rule, which it does not do. Thus Polearm Master does not work when somebody teleports into your reach. This stance is supported in the most-upvoted answer to the following question:
So then we've established that if blink counts as teleportation, you do not provoke an opportunity attack, and if it does not count as teleportation, you do provoke an opportunity attack.
Does blink count as teleporting? Maybe; ask your GM
The blink spell states:
[...] At the start of your next turn, and when the spell ends if you are on the Ethereal Plane, you return to an unoccupied space of your choice that you can see within 10 feet of the space you vanished from. [...]
The spell definitely involves planar travel, though this isn't the same thing as teleporting, however the spell also allows you to reappear at any space within 10 feet of where you left, which, at least to me, is effectively the same thing as teleporting. Though then there's also the case of reappearing in the exact same space you left from which is more complicated and not something I found hashed out in the rules. Whether returning from the Ethereal Plane through the blink spell counts as teleporting will ultimately be up to your GM.