See if they're with teachers' union when they arrive at hotel (5,4)

I believe the answer is:

check into

I'm a little stuck... Click here to teach me more about this clue!

'with teachers' union when they arrive at hotel' is the definition.
The definition suggests an adverb but the answer is not.

'see if' is the wordplay.
'see' becomes 'check' (synonyms).
'if' becomes 'into' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'check'+'into'='CHECK INTO'

'they're' is the link.

Can you help me to learn more?

I've seen this clue in The Irish Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.