Walk with Tony, first artist then MP (5)
I believe the answer is:
tramp
'walk' is the definition.
(tramp can mean to walk around)
'tony first artist then mp' is the wordplay.
'tony first' becomes 't' (1st letter of 'tony').
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'then' says to put letters next to each other.
't'+'ra'+'mp'='TRAMP'
'with' acts as a link.
(Other definitions for tramp that I've seen before include "Walk with heavy steps like hobo" , "Footslog" , "Bum!" , "one unlikely ever to have a mortgage!" , "Down-and-out" .)