Animal’s lair found by alien in street (4)
I believe the answer is:
sett
'animal's lair' is the definition.
(a sett is a badger's home)
'alien in street' is the wordplay.
'alien' becomes 'et' (extra terrestrial).
'in' is an insertion indicator.
'street' becomes 'st' (abbreviation).
'et' going inside 'st' is 'SETT'.
'found by' is the link.
(Other definitions for sett that I've seen before include "Badgers' lair" , "Underground 10 [HOUSE]" , "Badger's earth" , "Test for a badger's burrow" , "Badger's residence" .)