One man's best friend shattered his headlight's edges on no-frills Suzuki (4,3)
I believe the answer is:
shih tzu
'one man's best friend' is the definition.
(a dog is man's best friend)
'shattered his headlight's edges on no-frills suzuki' is the wordplay.
'shattered' is an anagram indicator.
'edges' suggests removing the centre (I've seen 'edges of' mean this).
'on' is a charade indicator (letters next to each other).
'no-frills' says to take the centre (edge letters or 'frills' are removed).
'headlight' with its middle removed is 'ht'.
The middle letters of 'suzuki' are 'zu'.
'his' is an anagram of 'shi'.
'shi'+'ht'+'zu'='SHIH-TZU'
(Another definition for shih tzu that I've seen is " Toy dog with long silky hair".)