If your fix term (eg 2%) ends on 31 December, from 01 January you will move into your mortgage lenders SVR - standard variable rate (eg 5%).
If you do nothing, your monthly mortgage rate will increase.
You can stay on this rate as long as you like. This is not usually recommended.
You can either remortgage with your existing mortgage lender (eg Halifax) or remortgage to a different lender (eg Barclays).
Each mortgage lender will have a range of mortgages (eg 4% fix for 3 years or 4.5% fix for 5 years).
It is recommended you go through an independent mortgage broker - L&C - to check the range of mortgages available to you (eg 4.5% with Halifax or 4.4% with Nationwide)
You then choose the mortgage that best suits your circumstances and your broker will arrange everything for you.
Check if you can overpay, and any early settlement fees.
It is usually recommended you try and remortgage 3 to 6 months before your current deal ends.