Mad king is engaged in winter sports (6)
I believe the answer is:
skiing
'winter sports' is the definition.
(I've seen this before)
'mad king is' is the wordplay.
'mad' indicates an anagram.
'king'+'is'='kingis'
'kingis' is an anagram of 'SKIING'.
'engaged in' is the 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 skiing that I've seen before include "going downhill, perhaps" , "Travelling over snow on runners" , "Mountain sport" , "Winter sports" , "going downhill fast" .)