Horrify a very quiet chap (5)
I believe the answer is:
appal
'horrify' is the definition.
(I know that horrify can be written as appal)
'a very quiet chap' is the wordplay.
'very quiet' becomes 'pp' (musical abbreviation for pianissimo).
'chap' becomes 'al' (man's name).
'a'+'pp'+'al'='APPAL'
(Other definitions for appal that I've seen before include "To shock, dismay" , "Greatly horrify" , "Disgust" , "Scandalise" , "Greatly dismay" .)