That is my situation. I got my 35 years in then stopped. I have it in writing that my
full pension will start early in the NY.
As I said before though, my sister paid NI contributions for 48 years but will NOT get the full new state pension because contracting out meant that many of her payments don't qualify.
Yes, she does get a private pension, BUT not what she was promised. She was told that she would get an X thousand pound lump sum and Y thousand pounds a year at the age of 60. Late in the day the government announced that, sorry, no state pension until you are 66. Oh, and X will now be reduced to a fraction of that. And... Y will be a lot less too. And to get those reduced payments, kindly carry on paying your pension and NI contributions for another 6 years...
You were born after April 1953, as was I, and this is the starting point for calculating the new state pension. People born earlier have their pension calculated on the, old, basic SP. Everyone has their state pension confirmed in writing regardless of which rules it's paid under.
It might be a good idea for your sister to speak to a financial adviser because there are conflicting statements in your post. If she has written evidence of a legally promised level of pension she needs advice on how to claim it. I would say it's highly unlikely such a promise will have been made.
Your sister contracted out of SERPS not the state pension. The element which was contracted out will have been used for a private pension so should not be counted twice when calculating state pension. It may be that element has not performed well but that's a risk everyone who contracted out took. My understanding is everyone should have been offered the opportunity to "contract in" if the private pension was underperforming against the Additional SP. This is something she may need advice on. I'd be surprised if she wasn't given the option but if she can prove this she may have a case against the provider.
Your final paragraph may be confusing private and state pension. As regards the private pension a provider would not, or at least should not, promise a given amount of either lump sum or annual income. There will have been illustration of the benefits based on projected contributions and growth. The way this is presented hasn't changed in perhaps 40 years. If your sister has evidence she was promised a level of pension which is now not going to be paid she should be considering action against the provider. Your sister will be expected to continue paying the (private) pension contributions till she retires to achieve the forecast value. Private pension forecasts are automatically based on this date, it's the law. The actual, final, value of a private pension is only known when one takes the pension prior to this it's simply a pot of money which varies daily according to market forces and the level of pension this buys is determined by the market on the day the pension is taken (crystalised is I think the term).
The other aspect of the private pension on which your sister may want to take advice is how to access those funds. It's no longer a question of simply buying an annuity (pension) and she will have several options. It's her money and how she chooses to spend it is her decision alone. If I use my own case I have chosen not to purchase an annuity but to access those funds as and when I wish in cash. Prior to reaching SP age I used drawdown to take out cash equal to the Personal Tax Allowance. Now I only drawdown sufficient to bring my income, SP + drawdown, up to the PTA. This means I don't pay tax. If there is a year when I need more money I drawdown more cash and pay tax in that year only. If I had purchased an annuity I would be above the PTA and paying tax, unnecessarily, every year.
For the majority much of this is straightforward once understood. If your sister is not getting what she expected she needs professional advice to understand her entitlement and options. There are a lot of very good financial advisors out there.
The change to women's SP age was very badly handled and along with hundreds of thousands of others she has every right to be angry.