Rope with which Henry gets cart pulled up (7)
I believe the answer is:
halyard
'rope' is the definition.
(I've seen this before)
'henry gets cart pulled up' is the wordplay.
'henry' becomes 'hal'.
'gets' says to put letters next to each other.
'cart' becomes 'dray' (a cart without sides for delivering heavy loads).
'pulled up' says the letters should be written in reverse.
'dray' back-to-front is 'yard'.
'hal'+'yard'='HALYARD'
'with which' is the link.
(Other definitions for halyard that I've seen before include "Sail-raising rope" , "Nautical rope" , "Line for hoisting a sail" , "(E.g. flag-raising) rope" , "Rope for hoisting a sail" .)