Start at least six games without an egghead (5)
I believe the answer is:
onset
'start' is the definition.
(both can mean the beginning of something)
'at least six games without an egghead' is the wordplay.
'at' becomes 'on' (location).
'least six games' becomes 'st' (I am not sure about this - if you are sure you should believe this answer much more).
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'an egghead' becomes 'e' (head letter of 'egg').
'st' enclosing 'e' is 'set'.
'on'+'set'='ONSET'
Can you help me to learn more?
(Other definitions for onset that I've seen before include "17 down [ASSAULT]" , "First signs" , "Appearance of" , "Beginning; military attack" , "Initial stage; attack" .)