Row over date's pedigree (7)
I believe the answer is:
lineage
'pedigree' is the definition.
(synonyms)
'row over date's' is the wordplay.
'row' becomes 'line' (as in a row of things).
'over' means one lot of letters go next to another (in a down clue, some letters go over others).
'date' becomes 'age' (both can mean to get older).
'line'+'age'='LINEAGE'
(Other definitions for lineage that I've seen before include "Ancestry, sequence of descendants" , "Line of descent or ancestry" , "Family descent" , "Descent (from an ancestor)" , "Stock" .)