Drop off family item used at table (6)
I believe the answer is:
napkin
'item used at table' is the definition.
(a napkin might be used at the dinner table)
'drop off family' is the wordplay.
'drop off' becomes 'nap' (I've seen this in another clue).
'family' becomes 'kin' (synonyms).
'nap'+'kin'='NAPKIN'
(Other definitions for napkin that I've seen before include "Cloth square worn while eating" , "Small piece of table linen" , "Diner's cloth" , "Cloth rectangle worn at mealtime" , "Protective cloth square donned during meals" .)