More irrelevant? Not half! (5)
I believe the answer is:
extra
'more' is the definition.
(thesaurus)
'irrelevant? not half' is the wordplay.
'irrelevant?' becomes 'extraneous' ('extraneous' can be similar in meaning to 'irrelevant').
'not half' indicates taking half.
'extraneous' with half the letters taken is 'EXTRA'.
(Other definitions for extra that I've seen before include "There's more" , "Another" , "Something additional or bit player in movie" , "Bonus; supplement" , "I may carry spear" .)