Begin again on meal, without starter of avocado (8)
I believe the answer is:
relaunch
'begin again' is the definition.
('launch' is an answer for 'begin' so perhaps 'relaunch' is OK for 'begin again')
'on meal without starter of avocado' is the wordplay.
'on' becomes 're' ('on' can be mean 'with reference to').
'meal' becomes 'lunch' (lunch is a kind of meal).
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'starter of' says to take the initial letters.
The initial letter of 'avocado' is 'a'.
'lunch' going around 'a' is 'launch'.
're'+'launch'='RELAUNCH'
(Other definitions for relaunch that I've seen before include "marketing operation" , "Begin (enterprise) again" , "Again introduce" , "New introduction of old product" .)