That man caught cold touring island, getting feverish (6)
I believe the answer is:
hectic
'feverish' is the definition.
('hectic' can be a synonym of 'feverish')
'that man caught cold touring island' is the wordplay.
'that man' becomes 'he'.
'caught' becomes 'ct'.
'cold touring island' becomes 'ic' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'he'+'ct'+'ic'='HECTIC'
'getting' is the link.
Can you help me to learn more?
(Other definitions for hectic that I've seen before include "Frantic or feverish" , "Marked by intense activity" , "Frantic, busy" , "Exciting, and confusing perhaps" , "Bustling" .)