Carry small child on one's back (4)
I believe the answer is:
tote
'carry' is the definition.
(I know that tote is a more specific form of carry)
'small child on one's back' is the wordplay.
'small child' becomes 'tot' (tot can mean a baby or toddler).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'back' suggests the final letters (the letter at the back).
The final letter of 'one' is 'e'.
'tot'+'e'='TOTE'
(Other definitions for tote that I've seen before include "It takes bets for horse races" , "hump" , "Form of betting: carry" , "Large bag" , "Bear" .)