Most tedious exam takes a minute (6)
I believe the answer is:
tamest
'most tedious' is the definition.
(tame can mean tedious or dull)
'exam takes a minute' is the wordplay.
'exam' becomes 'test' (synonyms).
'takes' is an insertion indicator.
'minute' becomes 'm' (abbreviation).
'a'+'m'='am'
'test' enclosing 'am' is 'TAMEST'.
(Other definitions for tamest that I've seen before include "Least wild, most domesticated" , "Meekest or least wild" , "Most docile" , "Most restrained or quiet" , "Least exciting" .)