One volunteers to accept nothing but a tiny bit (4)
I believe the answer is:
iota
'a tiny bit' is the definition.
(thesaurus)
'one volunteers to accept nothing' is the wordplay.
'one' becomes 'i' (Roman numeral).
'volunteers' becomes 'ta' (abbreviation for Territorial Army).
'to accept' means one lot of letters goes inside another.
'nothing' becomes 'o' (looks like zero - 0).
'i'+'ta'='ita'
'ita' going around 'o' is 'IOTA'.
'but' acts as a link.
(Other definitions for iota that I've seen before include "European letter" , "Gk. letter; tiny amount" , "(Not one) little bit" , "letter from abroad" , "Tiny bit" .)