Tenacious pursuer's blunder, entering bank (7)
I believe the answer is:
terrier
'tenacious pursuer's' is the definition.
'blunder entering bank' is the wordplay.
'blunder' becomes 'err' (I've seen this before).
'entering' is an insertion indicator.
'bank' becomes 'tier' (I've seen this before).
'err' going within 'tier' is 'TERRIER'.
(Other definitions for terrier that I've seen before include "One who volunteers to fight" , "See 11" , "Dog originally used to ferret out burrowing animals" , "Dog - old land register" , "Breed of dog - volunteer soldier - estate register" .)