Reportedly publicise weaving machine, something long in the family (8)
I believe the answer is:
heirloom
'something long in the family' is the definition.
(family heirloom)
'reportedly publicise weaving machine' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'publicise' becomes 'air' (airing is a kind of publicizing).
'weaving machine' becomes 'loom' (machine for weaving thread).
'air' is a homophone of 'heir'.
'heir'+'loom'='HEIRLOOM'
(Other definitions for heirloom that I've seen before include "Item handed down for years" , "Treasure handed down in family" , "Long-time family possession" , "one long in the family" , "Valuable object handed down" .)