Mention I construct housing of Greek style (5)
I believe the answer is:
ionic
'greek style' is the definition.
'Ionic' can be an answer for 'style' (I have seen 'Architectural style ' mean 'ionic' so perhaps 'style' could also mean 'ionic'). I am not sure about the 'greek' bit.
'mention i construct housing' is the wordplay.
'housing' indicates the answer is hidden within the clue (part of the clue houses the answer).
'IONIC' is hidden within 'mention i construct'.
'of' is the link.
Can you help me to learn more?
(Other definitions for ionic that I've seen before include "Classic order of architecture" , "Greek order" , "Like some Greek architecture" , "Style of Greek column used for the British Museum and the US Capitol" , "Classic form of dialect" .)
