Pass over the trumped-up story of the dog (6)
I believe the answer is:
collie
'the dog' is the definition.
(collie is a kind of dog)
'pass over the trumped-up story' is the wordplay.
'pass' becomes 'col' (col is a term for a mountain pass).
'over' says to put letters next to each other.
'the trumped-up story' becomes 'lie' (I've seen this in another clue).
'col'+'lie'='COLLIE'
'of' is the link.
(Other definitions for collie that I've seen before include "Working animal" , "Border dog" , "Farm dog" , "Sheepdog wth ling nose and shaggy hair" , "Silky-coated sheepdog" .)