Carry child on one's back (4)
I believe the answer is:
tote
'carry' is the definition.
(I know that tote is a kind of carry)
'child on one's back' is the wordplay.
'child' becomes 'tot' (term for a young child).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'back' indicates one should take the final letters (the letter at the back).
The last letter of 'one' is 'e'.
'tot'+'e'='TOTE'
(Other definitions for tote that I've seen before include "You can bet on this" , "Carry; betting device" , "Carry or shoulder" , "Carry to the betting machine" , "record of stakeholders' investments" .)