Story of a large wading bird with no tail (5)
I believe the answer is:
alibi
'story' is the definition.
(thesaurus)
'a large wading bird with no tail' is the wordplay.
'large' becomes 'l'.
'wading bird' becomes 'ibis' (ibis is a kind of wading bird).
'with no tail' means to remove the last letter.
'ibis' with its last letter removed is 'ibi'.
'a'+'l'+'ibi'='ALIBI'
'of' is the link.
(Other definitions for alibi that I've seen before include "Evidence one was elsewhere at time of crime" , "Excuse, in law" , "Court evidence showing one was elsewhere" , "that gets him off the hook?" , "Excuse for not doing something" .)