No carrying stone that’s unpleasant (5)
I believe the answer is:
nasty
'unpleasant' is the definition.
(nasty can mean unpleasant or horrible)
'no carrying stone' is the wordplay.
'no' becomes 'nay' (archaic form of 'no').
'carrying' is an insertion indicator.
'stone' becomes 'st' (abbreviation).
'nay' enclosing 'st' is 'NASTY'.
'that's' is the link.
(Other definitions for nasty that I've seen before include "Highly unpleasant" , "Not nice" , "Disgusting" , "One who sees the future" , "Beastly" .)