100 having examinations in which they have rivals (8)
I believe the answer is:
contests
'rivals' is the definition.
Although both the answer and definition are verbs in their -s form, I cannot see how one could define the other.
'100 having examinations in which they have' is the wordplay.
'o00' becomes 'C' (Roman numeral).
'having' is a charade indicator (letters next to each other).
'examinations' becomes 'tests' ('test' can be a synonym of 'examination').
'in which' is an insertion indicator.
'they have' becomes 'on' (I am not sure about this - if you are sure you should believe this answer much more).
'c'+'tests'='ctests'
'ctests' enclosing 'on' is 'CONTESTS'.
Can you help me to learn more?
(Other definitions for contests that I've seen before include "Disputes; competitions" , "Matches" , "Struggles between rivals" , "Competitions between rivals" , "Competitions, struggles" .)