That man caught cold touring island, getting feverish (6)
I believe the answer is:
Here is my best explanation:
'feverish' is the definition.
('hectic' can be a synonym of 'feverish')
'that man caught cold touring island' is the subsidiary indication.
'that man' becomes 'he' (**).
'caught' becomes 'ct'.
'cold' becomes 'c'.
'touring' indicates putting letters inside.
'island' becomes 'i'.
'ctc' going around 'i' is 'ctic'.
'getting' is the link.
(Other definitions for hectic that I've seen before include "Frantic, busy", "Involving feverish activity, flushed", "Chaotic or feverish", "in a rush", "'Extremely busy, rushed (6)'", "Frantically active", "Bustling", "With feverish activity", "Feverish" and "particularly busy".)