Sign at first and quibble, usually afterwards, when hybrid car doesn't start (8)
I believe the answer is:
aquarius
'sign' is the definition.
(Aquarius is an example)
'when hybrid car doesn't start' is the wordplay.
'when' becomes 'aqua' (I can't justify this - if you can you should give a lot more credence to this answer).
'hybrid car' becomes 'Prius' (Toyota Prius, a hybrid car).
'doesn't start' means to remove the first letter.
'prius' with its first letter removed is 'rius'.
'aqua'+'rius'='AQUARIUS'
'at first and quibble usually afterwards' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
(Other definitions for aquarius that I've seen before include "Sign of the zodiac, the water-bearer" , "Sign of the zodiac, the water-bearers" , "Sign of the water-carriers" , "The Water-carrier, 11th sign of the Zodiac" , "Zodiacal constellation" .)