The mortgage you have is specifically for you and your current property. Typically when you sell your solicitor receives the money from the purchaser, pays off the mortgage and gives you any surplus funds.
Regardless of what you do with your existing apartment any purchase of a new property will require a new mortgage (assuming you're not a cash purchaser). This mortgage will again be specifically for you for the new property. You will have to apply in a similar fashion as what you did 10 years ago.
When a lender assesses what they are willing to lend to you your age will be a factor. So is your income and also interest rates. All other things being equal the fact you are 10 years older (or 10 years closer to retirement) will likely lower the amount they would lend to you. If course you can't look at that in isolation. Your income may have also increased and interest rates will likely have decreased also.
10 years of meeting your mortgage repayments will very much count towards any new mortgage. In assessing you for a mortgage a lender will look through your bank statements, your income, your expenditure and any savings you have built up. From there they will work out what you can payback. Central Bank rules also limit you to 3.5 times your income. Though there are a limited number of exceptions lenders can make.
Something to remember is you've chipped away at your existing mortgage so you've built up your equity. Likewise over the last 10 years your apartment has probably gone up in value. This equity can be used for your new purchase. Again Central Bank rules require you, as a second time buyer, to fund 20% of the purchase price. Typically the proceeds from your apartment will go to funding this.