Rejecting volunteers, politician's swamped by mock test essays (8)
I believe the answer is:
attempts
'essays' is the definition.
('attempt' can be a synonym of 'essay')
'rejecting volunteers politician's swamped by mock test' is the wordplay.
'rejecting' is a reversal indicator.
'volunteers' becomes 'TA' (abbreviation for Territorial Army).
'politician' becomes 'MP' (Member of Parliament).
'swamped by' is an insertion indicator.
'mock' is an anagram indicator.
'ta' backwards is 'at'.
'test' is an anagram of 'tets'.
'mp' going into 'tets' is 'tempts'.
'at'+'tempts'='ATTEMPTS'
(Other definitions for attempts that I've seen before include "Endeavours, tries" , "Takes a shot" , "Efforts, endeavours" , "Makes a stab at" , "Has a go at" .)