Tarquin flustered at first later becoming calm (8)
I believe the answer is:
tranquil
'calm' is the definition.
(synonyms)
'tarquin flustered at first later' is the wordplay.
'flustered' indicates anagramming the letters.
'at' is a charade indicator (letters next to each other).
'first later' becomes 'l' (1st letter of 'later').
'tarquin' with letters rearranged gives 'tranqui'.
'tranqui'+'l'='TRANQUIL'
'becoming' acts as a link.
(Other definitions for tranquil that I've seen before include "Free from disturbance" , "Peaceful and quiet, not agitated" , "Peaceful - calm" , "Peaceful and serene" , "Calm and serene" .)