Act strangely on island, and go quiet (8)
I believe the answer is:
taciturn
'quiet' is the definition.
(thesaurus)
'act strangely on island and go' is the subsidiary indication.
'strangely' indicates an anagram.
'on' says to put letters next to each other.
'island' becomes 'i'.
'and' means one lot of letters go next to another.
'go' becomes 'turn' (turning is a kind of going**).
'act' anagrammed gives 'tac'.
'tac'+'i'+'turn'='taciturn'
(Other definitions for taciturn that I've seen before include "Tending to silence" , "Reserved, saying little" , "Tight-lipped" , "Not inclined to conversation" , "Disinclined to speak" .)