For the old pension, find out what type of pension it is. Defined Benefit or Defined Contribution, Defined Benefit schemes are often provided by NHS, Military, Teaching, Local and National Government, some very large companies. Defined Contribution are the the schemes which most other places use.
With Defined Benefit you pay in money but you are not building a pot of money for yourself, instead you get the promise of a benefit amount, paid to you every year for the rest of your life. With defined contribution, you build up a pot of money, which is invested, and then you take money out of that pot and when it is empty that is it all gone.
If it is a defined contribution scheme you can transfer it to another defined contribution scheme... so you merge small pensions to keep the admin tidy and the costs low.
With your new pension, find out if by paying in more that your employer pays in more. They probably won't pay in more, The amount they pay in is often based on your salary, so as your salary goes up, the employer contribution goes up.
Paying more to pension is nearly always the best thing to do, long term. However you need to think about short term things as well, such as having an emergency fund, not having debt, and known upcoming big expenses.
Video: Pension vs saving in ISA.