Complaint of an irrational prig at the back of the queue (5)
I believe the answer is:
gripe
'complaint' is the definition.
(thesaurus)
'an irrational prig at the back of the queue' is the wordplay.
'an irrational' indicates anagramming the letters.
'at the back of' indicates one should take the final letters (I've seen 'at the back' mean this).
The final letter of 'queue' is 'e'.
'prig' is an anagram of 'grip'.
'grip'+'e'='GRIPE'
'of' is the link.
(Other definitions for gripe that I've seen before include "Grumble (colloq.)" , "Complain; stomach pain" , "Keep on complaining" , "Complain; colic (water)" , "Protest" .)