Analyse eejit on the outskirts of Athenry (5)
I believe the answer is:
assay
'analyse' is the definition.
(assaying is a kind of analysing)
'eejit on the outskirts of athenry' is the wordplay.
'eejit' becomes 'ass' (I can't explain this - if you can you should believe this answer much more).
'on' says to put letters next to each other.
'the outskirts of' says to hollow out the word (remove centre letters) (letters on the edges or outskirts are used).
'athenry' with its middle removed is 'ay'.
'ass'+'ay'='ASSAY'
Can you help me to learn more?
(Other definitions for assay that I've seen before include "Check (a metal's) quality" , "Test the purity of metals" , "Test, check" , "Put to the proof" , "Evaluate" .)