The wreckage of many buried in brief notoriety (7)
I believe the answer is:
flotsam
'the wreckage' is the definition.
(flotsam is a kind of wreckage)
'many buried in brief notoriety' is the wordplay.
'many' becomes 'lots' (lots of something).
'buried in' means one lot of letters goes inside another (inserted letters get buried).
'brief' means to remove the last letter (a shorter or briefer version of the word).
'notoriety' becomes 'fame' (I've seen this in another clue).
'fame' with its final letter taken away is 'fam'.
'lots' inserted within 'fam' is 'FLOTSAM'.
'of' is the link.
(Other definitions for flotsam that I've seen before include "Detritus" , "Wreckage found floating" , "Wreck" , "The floating wreckage of a ship" , "Things found floating from a ship" .)