Lively deliveries essentially following start of play (6)
I believe the answer is:
active
'lively' is the definition.
(similar in meaning)
'deliveries essentially following start of play' is the wordplay.
'deliveries' becomes 'over' (I've seen this before).
'essentially' indicates the central letters.
'following' says to put letters next to each other.
'start of play' becomes 'act i' (Act I).
The middle of 'over' is 've'.
've' after 'acti' is 'ACTIVE'.
(Other definitions for active that I've seen before include "Lively, working away" , "Busy, not idle" , "Busy, energetic" , "Working; moving" , "Moving, doing things" .)