Offspring in the vicinity of house initially left embracing in snug place (5-4)
I believe the answer is:
cubby-hole
'snug place' is the definition.
(I've seen this before)
'offspring in the vicinity of house initially left embracing' is the wordplay.
'offspring' becomes 'cub' (cub is a kind of offspring).
'in the vicinity of' becomes 'by' ('by' can mean next to or near).
'house' becomes 'h'.
'initially left embracing' becomes 'ole' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'cub'+'by'+'h'+'ole'='CUBBY-HOLE'
'in' is the link.
Can you help me to learn more?
(Another definition for cubby-hole that I've seen is " Small compartment".)