Hardly bringing ton up (3)
I believe the answer is:
not
'hardly' is the definition.
'ton up' is the wordplay.
'up' says the letters should be written backwards (in down clue: letters go upwards).
'ton' written backwards gives 'NOT'.
'bringing' is the link.
(Other definitions for not that I've seen before include "Negation of what follows" , "logically, operation needed" , "Having close-cut hair" , "It negates a word" , "In no way, never" .)