Aristocrat has way to annoy (6)
I believe the answer is:
pester
'annoy' is the definition.
(thesaurus)
'aristocrat has way' is the wordplay.
'aristocrat' becomes 'peer' (peer is a kind of aristocrat).
'has' indicates putting letters inside.
'way' becomes 'st'.
'peer' going around 'st' is 'PESTER'.
'to' is the link.
(Other definitions for pester that I've seen before include "Bug" , "Annoy persistently" , "Annoy with persistent requests" , "Be a nuisance, annoy with requests" , "Trouble, annoy" .)