Yes you can!
If you have purchased an item within the last 3 months in one of our stores whilst in the UK, but live in the Republic of Ireland, you are entitled to a refund of VAT. You can ask for a VAT Refund Form from any New Look store which you will need to hand into the UK Airport/Border VAT office to disclose this alongside your receipt, and receive the refund before you exit the UK.
You are unable to make a claim for VAT if you have left the UK and do not intend to return within 3 months of the purchase date.