Wild horse carrying leader on desert island (6)
I believe the answer is:
rhodes
'island' is the definition.
(Greek island)
'wild horse carrying leader on desert' is the wordplay.
'wild' is an anagram indicator.
'carrying' indicates putting letters inside.
'leader on' says to take the initial letters (the letter which leads the word).
The first letter of 'desert' is 'd'.
'horse' anagrammed gives 'rhoes'.
'rhoes' placed around 'd' is 'RHODES'.
(Other definitions for rhodes that I've seen before include "Greek port" , "British financier and coloniser in southern Africa, d. 1902" , "Greek island, ten miles off the Turkish coast" , "Horsed around on the Greek island" , "See 21 Down" .)