Isn’t involved in the most significant claim (8)
I believe the answer is:
maintain
'claim' is the definition.
(thesaurus)
'isn't involved in the most significant' is the wordplay.
'isn't' becomes 'aint' (I've seen this before).
'involved in' means one lot of letters goes inside another.
'the most significant' becomes 'main'.
'aint' inserted inside 'main' is 'MAINTAIN'.
(Other definitions for maintain that I've seen before include "Keep in safety and protect from harm and decay" , "Keep in existence or in repair" , "declare" , "Keep going" , "Look after the upkeep" .)