Yes you can!
You are entitled to a refund of VAT of in store purchases, as long as you meet the following:
The spend must be £25 or more to qualify.
You MUST live in the Republic of Ireland.
You MUST be leaving the UK within 4 months of the purchase date.
You can ask for a VAT Refund Form or complete the Tax Free Digital form (in selected stores) in the New Look store when you make your purchase.
You will then need to provide this form alongside your item(s) and receipt, at the UK Airport VAT office to disclose this and receive the refund before you exit the UK.
Please note: You are unable to make a claim for VAT if you have left the UK and do not intend to return within 4 months of the purchase date.