The old king is shrewd about an introduction (6)
I believe the answer is:
canute
'the old king' is the definition.
(medieval Danish king)
'about an introduction' is the wordplay.
'about' becomes 'c' (abbreviation for 'circa').
'introduction' becomes 'ute' (I am not sure about this - if you are sure you should believe this answer much more).
'c'+'an'+'ute'='CANUTE'
'is shrewd' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for canute that I've seen before include "Danish king of England who tried to stop the tide" , "King of England, Denmark and Norway" , "The king who thought he could stop the tide" , "King of England (1016)" , "The king who couldn't stop the tide" .)