You are correct that cannot back-date the pension contribution and thus claim back tax already paid.
But see
https://www.gov.uk/tax-on-your-private-pension/annual-allowanceYou can therefore use this 13K of net (i.e. after taxation) income from last year to offset your tax liability this year
subject to a maximum of 40K total annual pension contribution (which you may already be making?)
Your pension provider will automatically claim back the 20% basic rate directly from the government when you make a contibution from net income.
You can then claim back any higher-than-20% tax paid on this same net pension contribution.
The 2% National Insurance Contribution on the 13K is permanently lost I am afraid.
And I am simultaneously both happy for you, and sad for you, that you are well enough remunerated that you get caugt in the UK's 60% marginal taxation trap.
(Personally I always "maxed-out" my pension contribution rate to never quite get caught by even the 40% tax rate)