A riotous stay out East with a poet (5)
I believe the answer is:
yeats
'a poet' is the definition.
(Yeats is an example)
'a riotous stay out east' is the wordplay.
'a riotous' is an anagram indicator.
'out' indicates putting letters inside.
'east' becomes 'e' ('E' can be a synonym of 'east').
'stay' is an anagram of 'yats'.
'yats' placed around 'e' is 'YEATS'.
'with' is the link.
(Other definitions for yeats that I've seen before include "William Butler ....., poet and dramatist" , "Irish poet, 1923 Nobel Prize winner" , "William Butler ..., great Irish poet" , "Irish poet (The Winding Stair)" , "William Butler .. . . ., Nobel-winning poet" .)