If the company you work for is registered in the UK and they don't have an office and bank accounts in Gibraltar, plus you would be working from home, I assume they would still pay you your wages in the UK to your UK bank account, still under UK PAYE, so no change for you!
If they do however have a separate business entity in Gibraltar and you would be employed by them, unless they give you a substantial pay rise you salary will somewhat less after tax, depending on how much you earn.
In Gibraltar income tax is 30%-35% of your income.