Crossword Genius

We hear a noisy argument over the reportedly expensive animal (3,4)

Ross

I believe the answer is:

roe deer

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

'animal' is the definition.
(I've seen this before)

'we hear a noisy argument over the reportedly expensive' is the wordplay.
'we hear' becomes 'e' (I've seen this in other clues).
'a noisy argument' becomes 'ro' (I am not sure about this - if you are sure you should believe this answer much more).
'over' says to put letters next to each other.
'the reportedly' shows a homophone (sound like).
'expensive' becomes 'dear' (similar in meaning).
'dear' is a homophone of 'deer'.
'e' put after 'ro' is 'roe'.
'roe'+'deer'='ROE-DEER'

Can you help me to learn more?

(Other definitions for roe deer that I've seen before include "Small (antlered) mammal" , "Small antlered animal(s)" , "Ruminant, reddish in summer" , "Brute" , "Hoofed animal(s)" .)

I've seen this clue in The Hindu.
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