Most retiring set out after quiet end to party (6)
I believe the answer is:
shyest
'most retiring' is the definition.
(I've seen this before)
'set out after quiet end to party' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'after' says to put letters next to each other.
'quiet' becomes 'sh' (**).
'end to' indicates one should take the final letters.
The final letter of 'party' is 'y'.
'set' is an anagram of 'est'.
'sh'+'y'='shy'
'est' after 'shy' is 'SHYEST'.
(Other definitions for shyest that I've seen before include "Most reticent" , "Most bashful or self-conscious" , "Most retiring" , "Most timid" , "Most diffident" .)