Fail to notice one on purpose (7)
I believe the answer is:
mission
'purpose' is the definition.
(I know that purpose can be written as mission)
'fail to notice one on' is the wordplay.
'fail to notice' becomes 'miss' (I've seen this in another clue).
'one' becomes 'I' (Roman numeral).
'miss'+'i'+'on'='MISSION'
(Other definitions for mission that I've seen before include "Task assigned to be done" , "Ministry sent by a church to spread its teaching" , "Very dangerous assignment -- Tom Cruise film series" , "Important assignment" , "Delegation" .)