Tease a lord, being heartless and vulgar (6)
I believe the answer is:
ribald
'vulgar' is the definition.
(thesaurus)
'tease a lord being heartless' is the wordplay.
'tease' becomes 'rib' (I've seen this before).
'being heartless' means to remove the middle letters.
'lord' with its centre taken out is 'ld'.
'rib'+'a'+'ld'='RIBALD'
'and' is the link.
(Other definitions for ribald that I've seen before include "Coarsely mocking" , "Humorous in vulgar or disrespectful way" , "Humourous in vulgar way" , "Funny, but not nice" , "Scurrilous, bawdy" .)