Weight carried by expert without hesitation (2,4)
I believe the answer is:
at once
'without hesitation' is the definition.
(I've seen this in another clue)
'weight carried by expert' is the wordplay.
'weight' becomes 'ton' (unit of weight).
'carried by' indicates putting letters inside.
'expert' becomes 'ace' (ace can informally mean very good).
'ton' inserted inside 'ace' is 'AT ONCE'.
(Other definitions for at once that I've seen before include "A no etc (anag)" , "without hesitation" , "'Without delay (2,4)'" , "simultaneously" , "Right now, this instant" .)