Informal footwear on one backward holiday island (5)
I believe the answer is:
naxos
'holiday island' is the definition.
'naxos' can be an answer for 'island' (I've seen this before). I am not sure about the 'holiday' bit.
'informal footwear on one backward' is the wordplay.
'informal footwear' becomes 'sox' (I can't justify this - if you can you should give a lot more credence to this answer).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'one' becomes 'an' (an apple is one apple).
'backward' shows that the letters should be reversed in order.
'sox'+'an'='soxan'
'soxan' in reverse letter order is 'NAXOS'.
Can you help me to learn more?
(Another definition for naxos that I've seen is " Island where Theseus abandoned Ariadne".)