On ice, finally, slip carelessly, causing swelling (4)
I believe the answer is:
node
'swelling' is the definition.
(swelling on the body)
'on ice finally slip carelessly' is the wordplay.
'on' means one lot of letters go next to another.
'finally' indicates one should take the final letters.
'slip carelessly' becomes 'nod' (to nod can mean to make a careless error).
The last letter of 'ice' is 'e'.
'e' put after 'nod' is 'NODE'.
'causing' acts as a link.
(Other definitions for node that I've seen before include "Where network lines meet" , "Natural swelling of part of a plant or animal" , "Point at which several lines come together" , "growth" , "Point of branching in a network" .)