Tour outskirts with popular, single father on Caribbean island (8)
I believe the answer is:
trinidad
'caribbean island' is the definition.
(I've seen this before)
'tour outskirts with popular single father' is the wordplay.
'outskirts' suggests removing the centre (I've seen 'outskirts of' mean this).
'with' means one lot of letters go next to another.
'popular' becomes 'in' ('in' can mean trendy).
'single' becomes 'I' (one).
'father' becomes 'dad' (informal term for father).
'tour' with its middle taken out is 'tr'.
'tr'+'in'+'i'+'dad'='TRINIDAD'
'on' is the link.
(Other definitions for trinidad that I've seen before include "... [WI ISLAND]" , "English-speaking island off Venezuela" , "West Indian island paired with Tobago" , "Island linked to Tobago" , "W. I. island" .)