Cover provided by second family (4)
I believe the answer is:
skin
'cover' is the definition.
(I know that skin is a type of body covering)
'by second family' is the wordplay.
'by' is a charade indicator (letters next to each other).
'second' becomes 's' (common abbreviation).
'family' becomes 'kin' (synonyms).
's' next to 'kin' is 'SKIN'.
'provided' acts as a link.
(Other definitions for skin that I've seen before include "Remove the outer layer" , "Dermis" , "Fell" , "Surface layer" , "Scrape, as the knee" .)