Cani recalim vat even though I dont have an invoice?

I run a business and pay certain people who dont invoice me for there services. I am I able to claim the vat back for these payments. The people in question are performers and tax exempt, under Irish law for artists.

By tax exempt do you mean VAT exempt? If so you can't reclaim VAT as it was not paid.
You can only reclaim VAT if the person being paid has registered for VAT and has charged you VAT.
Also - in England at least you cannot reclaim VAT unless you have a VAT receipt.

Not without an orginal receipts. Is it alot of money, if so, you might able to deduct from your tax return. But again, without a receipt, you can not do anything

If they are not registered for VAT then they can not charge you VAT as it must be itemised on any invoice and have the VAT registration number on that invoice.
You can not calim any VAT back fro which you do not have a receipt.
I would be concerned that you a are apparently paying out monies detailed as VAT to non registered persons and therefore they are acting outside the law.

You need an invoice from them try reducing their bill by 17.5% every time see how long it takes them to produce a proper invoice.