Air of sailor briefly showing temper (6)
I believe the answer is:
'temper' is the definition.
'air of sailor briefly' is the wordplay.
'air of sailor' becomes 'sea song' (a song sung at sea - air can mean a tune).
'briefly' means to remove the last letter.
'seasong' with its last letter taken off is 'SEASON'.
'showing' is the link.
(Other definitions for season that I've seen before include "Add flavouring", "eg Winter", "Spring, say", "Eg, summer", "One of four periods".)