Lair dug, excavation nearby starts (3)
I believe the answer is:
den
'lair' is the definition.
('den' can be a synonym of 'lair')
'dug excavation nearby starts' is the wordplay.
'starts' indicates taking the first letters.
The initial letters of 'dug excavation nearby' is 'DEN'.
(Other definitions for den that I've seen before include "Home of the beast" , "Miserable place" , "Animal shelter" , "Animal's lair or man's study" , "Lair for animal or study for gent" .)