Tattered cover did split (8)
I believe the answer is:
divorced
'split' is the definition.
(split up)
'tattered cover did' is the wordplay.
'tattered' is an anagram indicator.
'cover'+'did'='coverdid'
'coverdid' with letters rearranged gives 'DIVORCED'.
(Other definitions for divorced that I've seen before include "separated" , "Of married couple, legally parted" , "disbanded union" , "Of marriage, legally terminated" , "No longer married" .)