Service essentially settles each part of tennis game (3,3)
I believe the answer is:
tea set
'service' is the definition.
(service can mean items for serving tea)
'essentially settles each part of tennis game' is the wordplay.
'essentially' says to take the centre.
'each' becomes 'ea' (abbreviation).
'part of tennis game' becomes 'set' (I can't justify this - if you can you should believe this answer much more).
The centre of 'settles' is 't'.
't'+'ea'+'set'='TEA-SET'
Can you help me to learn more?
(Other definitions for tea set that I've seen before include "Matching plates, cups, etc" , "China for small meal" , "Estate (anag) - service" , "Collections of cups, saucers etc for serving light meal" , "facility for refreshment" .)