Pedigree Pomeranian's tail interrupting story time (7)
I believe the answer is:
lineage
'pedigree' is the definition.
('lineage' can be a synonym of 'pedigree')
'pomeranian's tail interrupting story time' is the wordplay.
'tail' indicates one should take the final letters.
'interrupting' indicates putting letters inside.
'story' becomes 'lie' (I've seen this before).
'time' becomes 'age' (age is a kind of time).
The final letter of 'pomeranian' is 'n'.
'n' going within 'lie' is 'line'.
'line'+'age'='LINEAGE'
(Other definitions for lineage that I've seen before include "Ancestral line as seen in eagle" , "Direct descent" , "Ancestry, sequence of descendants" , "Stock" , "Genealogy" .)