What may have been sung with tear seen flowing (8)

I believe the answer is:

serenate

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

'what may have been sung' is the definition.
I know nothing about this answer so I can't tell whether this works.

'with tear seen flowing' is the wordplay.
'with' means one lot of letters go next to another.
'flowing' indicates anagramming the letters.
'tear'+'seen' is 'tearseen'.
'tearseen' is an anagram of 'SERENATE'.

Can you help me to learn more?

I've seen this clue in The 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.