Overhears support for gutters and sinks (10)

I believe the answer is:

eavesdrops

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

'overhears support' is the definition.
I can't tell whether this definition defines the answer.

'gutters and sinks' is the wordplay.
'gutters' becomes 'eaves' (I can't justify this - if you can you should believe this answer much more).
'and' says to put letters next to each other.
'sinks' becomes 'drops' ('drop' can be a synonym of 'sink').
'eaves'+'drops'='EAVESDROPS'

'for' acts as a link.

Can you help me to learn more?

(Other definitions for eavesdrops that I've seen before include "taps" , "Earwigs" .)

I've seen this clue in the Sydney Morning Herald.

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.