Quite composed, though possibly teased (6)
I believe the answer is:
sedate
'quite composed' is the definition.
'sedate' can be an answer for 'composed' (I've seen this before). I am not certain of the 'quite' bit.
'possibly teased' is the wordplay.
'possibly' indicates an anagram.
'teased' is an anagram of 'SEDATE'.
'though' is the link.
Can you help me to learn more?
(Other definitions for sedate that I've seen before include "Quiet and dignified" , "Placid" , "Staid - tranquillise" , "Dignified and subdued" , "Teased into being calm" .)