Seek private place, largely at first for one’s replacement PIN (6,3)
I believe the answer is:
wooden leg
'replacement pin' is the definition.
(pin can informally mean a leg)
'seek private place largely at first for one's' is the wordplay.
'seek' becomes 'woo' (to woo is to seek or pursue romantically).
'private place' becomes 'den'.
'at first' says to take the initial letters.
'for one' becomes 'eg' (I've seen this in other clues).
The first letter of 'largely' is 'l'.
'woo'+'den'+'l'+'eg'='WOODEN LEG'
(Other definitions for wooden leg that I've seen before include "Eight lines of verse" , "Walk-on part" .)