It gives the pedigree one row at a time (7)
I believe the answer is:
lineage
'it gives the pedigree one' is the definition.
The definition suggests a singular noun which matches the answer.
'row at a time' is the wordplay.
'row' becomes 'line' (I've seen this before).
'at' is a charade indicator (letters next to each other).
'a time' becomes 'age' (age is a kind of time).
'line'+'age'='LINEAGE'
Can you help me to learn more?
(Other definitions for lineage that I've seen before include "Ancestry, sequence of descendants" , "Descent from ancestors" , "Pedigree, family tree" , "The strain" , "Direct descent" .)