Hi L. Czekala,
Your employer is not liable to pay tax in Spain. You are. Your gross employment income should be declared in Spain, so that it can be taxed appropriately in that country. As you are not UK resident, your employment income will not have national insurance deducted.
If you want to pay NIC towards your state pension, then you will need to contact the NIC helpline for advice (+44 19 1225 4811 from outside the UK).
You will need to complete form P85 (if you have not already done so) to declare that you are no longer resident in the UK and that you still have live UK employment.
Get your Income Tax right if you're leaving the UK (P85)
This will allow your employer to receive a tax code advising that they do not need to deduct UK tax from your income.
Thank you.