Pine tar soap finally running out (4)
I believe the answer is:
itch
'pine' is the definition.
(to pine for and to itch for both mean to desire)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for itch that I've seen before include "minor irritant" , "Seven-yearly desire" , "following seven years in union?" , "burn" , "Strong desire to do something" .)