Shorten story heard in support of vicious dog (7)
I believe the answer is:
curtail
'shorten' is the definition.
(curtailing is a kind of shortening)
'story heard in support of vicious dog' is the wordplay.
'story' becomes 'tale' ('tale' can be a synonym of 'story').
'heard' indicates a 'sounds like' (homophone) clue.
'in support of' is a charade indicator (letters next to each other) (I've seen this in other clues).
'vicious dog' becomes 'cur' (I've seen this before**).
'tale' is a homophone of 'tail'.
'tail' after 'cur' is 'CURTAIL'.
(Other definitions for curtail that I've seen before include "Dock" , "'Cut short, restrict (7)'" , "Impose a restriction on" , "Shorten, abridge" , "Abbreviate" .)