Invitation to compete with your setter β in flower arrangement? (6)
I believe the answer is:
raceme
'flower arrangement?' is the definition.
(I've seen this before)
'invitation to compete' is the wordplay.
'invitation' becomes 'me' (I can't justify this - if you can you should believe this answer much more).
'to' is a charade indicator (letters next to each other) (I've seen this in other clues).
'compete' becomes 'race' (racing is a kind of competing).
'me' put after 'race' is 'RACEME'.
'with your setter in' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
(Other definitions for raceme that I've seen before include "something flowery" , "Long cluster of flowers along the main stem" , "Flowers evenly spaced along central stem" , "flower arrangement" , "Flower cluster (botany)" .)