Threw a pest out of Preston's north end (5)
I believe the answer is:
slung
'threw' is the definition.
(I've seen this before)
'a pest out of preston's north end' is the wordplay.
I cannot quite see how this works, but
'north' could be 'n' (abbreviation) and 'n' is present in the answer.
'pest' could be 'slug' (I've seen this before) and 'slug' is found in the leftover letters.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for slung that I've seen before include "Thrown; suspended loosely" , "Hurled" , "Threw out" .)