Crossword Genius

Reportedly hear military engineers constructing an ancient warship (7)

Ross

I believe the answer is:

trireme

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

'an ancient warship' is the definition.
(I've seen this in another clue)

'reportedly hear military engineers' is the wordplay.
'reportedly' shows a homophone (sound like).
'hear' becomes 'try' (to hear or try a case in the legal sense).
'military engineers' becomes 'REME' (Royal Electrical and Mechanical Engineers).
'try' sounds like 'tri'.
'tri'+'reme'='TRIREME'

'constructing' is the link.
This may not be correct. It may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for trireme that I've seen before include "Ancient Greek or Roman war galley" , "Ancient vessel with three banks of oars on each side" , "Roman/Greek galley" , "Oar-driven battleship of classical times" , "Greek warship" .)

I've seen this clue in The Times.
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