Landowner to burrow deeper, initially (5)
I believe the answer is:
laird
'landowner' is the definition.
(Scottish term for a landowner)
'burrow deeper initially' is the wordplay.
'burrow' becomes 'lair' (I've seen this before).
'initially' indicates taking the first letters.
The initial letter of 'deeper' is 'd'.
'lair'+'d'='LAIRD'
'to' acts as a link.
(Other definitions for laird that I've seen before include "One's landed in Scotland" , "rich Scotsman" , "Proprietor" , "He's landed in Scotland" , "Scots estate owner" .)