You'll need to be more precise!
Are you talking about back dating contributions missed to the state pension, or a company scheme, or a private pension? Or are you set up as a limited company?
State has specific rules, but yes. Company scheme will depend on the rules. Limited companies have their own legislation.
If you mean a personal defined contribution scheme then yes, you can back date payments - sort out!
It's actually called a carry forward.
Your annual allowance that you can get tax relief on in one tax year is £40K or your total earned income - whichever is lower.
You can carry forward the previous 3 years of £40K allowance - but:
- only if you held a pension other than a state pension during that time. Doesn't have to have had any contributions, but it had to exist. You can't just open a personal pension tomorrow and use the carry forward.
- your tax relief is limited to your current year earned income.
So if you earned £30K per year you could add £90K to your pension. But you'd only get tax relief on the tax paid in current year: £30K less your personal tax allowance. You couldn't add £90K and get tax relief on it all.
You say you earn a tiny amount... if that means you're not paying tax this year, then there's no tax relief reason to use your carry forward. An ISA would give you the same fund options, and you would be taxed on the way out and it would be more flexible.
As I say - more detail needed!