Mike secretly embracing the Italian racket in construction (8)
I believe the answer is:
Here is my best explanation:
'construction' is the definition.
(building is a kind of construction)
'mike secretly embracing the italian racket' is the wordplay.
'mike secretly' becomes 'bug' (I am not sure about this - if you are sure you should believe this answer much more).
'embracing' means one lot of letters goes inside another.
'the italian' becomes 'il' (the in Italian).
'racket' becomes 'din' (I've seen this before).
'bug' going around 'ildin' is 'BUILDING'.
'in' acts as a link.
(Other definitions for building that I've seen before include "Construction", "Constructing", "Structure, edifice", "Erection", "Structure with roof and walls" and "Edifice".)