More precise haulier ditching fashion label (5)
I believe the answer is:
truer
'more precise' is the definition.
(more true)
'haulier ditching fashion label' is the wordplay.
'haulier' becomes 'trucker' (someone driving a haulage truck).
'ditching' is a deletion indicator.
'fashion label' becomes 'CK' (Calvin Klein).
'trucker' with 'ck' removed is 'TRUER'.
(Other definitions for truer that I've seen before include "More in accordance with fact" , "More faithful or straight" , "That's more like it" , "More accurate" , "More relaible" .)