Begin a fight after series of tennis games (3,5)
I believe the answer is:
set about
'begin' is the definition.
('set about' can be a synonym of 'begin')
'a fight after series of tennis games' is the wordplay.
'fight' becomes 'bout' ('bout' can be a synonym of 'fight').
'after' means one lot of letters go next to another.
'series of tennis games' becomes 'set' (I've seen this before).
'a'+'bout'='about'
'about' put after 'set' is 'SET ABOUT'.
(Other definitions for set about that I've seen before include "Start to do something with determination" , "Get cracking" , "Begin - attack" , "Embark upon" .)