GOP grandees can rage about old school competition (3-3-5,4)
I believe the answer is:
egg-and-spoon race
'school competition' is the definition.
(informal race at a school sports day)
'gop grandees can rage about old' is the wordplay.
'rage' indicates anagramming the letters.
'about' indicates putting letters inside.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'gop'+'grandees'+'can'='gopgrandeescan'
'gopgrandeescan' is an anagram of 'eggandsponrace'.
'eggandsponrace' placed around 'o' is 'EGG-AND-SPOON RACE'.
(Another definition for egg-and-spoon race that I've seen is " Handicapped running contest".)