Regularly taking volleys - initially most players improve action during school games periods (9)

'games periods' is the definition.
(periods between Olympic games)

'regularly taking volleys initially most players improve action during' is the wordplay.
'regularly taking' means one should take alternating letters.
'initially' indicates taking the first letters.
'during' becomes 'ds' (I can't justify this - if you can you should believe this answer much more).
The initial letters of 'most players improve action' is 'mpia'.
The alternate letters of 'volleys' are 'oly'.
'oly'+'mpia'+'ds'='OLYMPIADS'

'school' is the link.
This may not be correct. It may be part of another bit of the clue.