Notion, however, irrelevant in the end (7)
I believe the answer is:
thought
'notion' is the definition.
(I've seen this before)
'however irrelevant in the end' is the wordplay.
'however' becomes 'though' (synonyms).
'in the end' indicates one should take the final letters.
The last letter of 'irrelevant' is 't'.
'though'+'t'='THOUGHT'
(Other definitions for thought that I've seen before include "That's an idea" , "Idea, concept" , "Idea coming to mind" , "Philosopher must master this" , "Mental idea" .)