Inheritance gift of frilly clothing for example (6)
I believe the answer is:
legacy
'inheritance gift' is the definition.
(gift left in someone's will)
'frilly clothing for example' is the wordplay.
'frilly' becomes 'lacy' (I've seen this in other clues).
'clothing for' means one lot of letters goes inside another.
'example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'lacy' going around 'eg' is 'LEGACY'.
'of' is the link.
(Other definitions for legacy that I've seen before include "Hand-me-down" , "Birthright" , "Heritage" , "Something bequeathed in will" , "Bombay since 1995" .)