Time after row involving pedigree (7)
I believe the answer is:
lineage
'pedigree' is the definition.
(I know that pedigree can be written as lineage)
'time after row' is the wordplay.
'time' becomes 'age' (an age is a period of time).
'after' says to put letters next to each other.
'row' becomes 'line' (as in a row of things).
'age' put after 'line' is 'LINEAGE'.
'involving' acts as a link.
(Other definitions for lineage that I've seen before include "Family descent" , "Descent from ancestors" , "Descent (from an ancestor)" , "Line of descent or ancestry" , "Stock" .)