A first grade finish a list of things to be done (6)
I believe the answer is:
agenda
'list of things to be done' is the definition.
(I've seen this before)
'a first grade finish a' is the wordplay.
'first grade' becomes 'g' (1st letter of 'grade').
'finish' becomes 'end' (synonyms).
'a'+'g'+'end'+'a'='AGENDA'
(Other definitions for agenda that I've seen before include "List of matters to be discussed at a meeting" , "Items of business for committee meeting" , "To-do list" , "Table of business" , "Items for discussion at committee meeting" .)