Home of old duke in Lincoln (5)
I believe the answer is:
abode
'home' is the definition.
(synonyms)
'old duke in lincoln' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'duke' becomes 'd' (abbreviation).
'in' means one lot of letters goes inside another.
'lincoln' becomes 'abe' (Abraham Lincoln).
'o'+'d'='od'
'od' inserted within 'abe' is 'ABODE'.
'of' acts as a link.
(Other definitions for abode that I've seen before include "House, home" , "Dwelling, residence" , "stay" , "Home or domicile" , "Where one lives" .)