Game played by good university teacher (4)
I believe the answer is:
guru
'teacher' is the definition.
(teacher or guide)
'game played by good university' is the wordplay.
'game played' becomes 'RU' (rugby union).
'by' means one lot of letters go next to another.
'good' becomes 'g' (abbreviation).
'university' becomes 'u' (abbreviation for university).
'g'+'u'='gu'
'ru' put after 'gu' is 'GURU'.
(Other definitions for guru that I've seen before include "Recognised expert in some field" , "Wise leader" , "Revered mentor" , "Hindu or Buddhist spiritual teacher" , "Spiritual teacher, mentor" .)