Income tax is calculated on an annual basis, from April 6th to April 5th the next year (a so-called "tax year"), but withheld from each payslip ("PAYE") so you don't have to pay it all at the end of the year.
As a result, if your pay changes mid-year sometimes the month by month deductions won't be the same as if you had been paid the same amount each month. For example, in your case, your previous salary after taking off pension contributions was less than the higher-rate tax threshold of £50,000. So you have some "unused" basic-rate band (i.e. the amount up to the higher-rate threshold) from the first months of the tax year. That's now being applied to some of your pay that you'd otherwise be paying higher-rate tax on.
As of your April pay, you should expect your take-home pay to be consistent with salary calculators, assuming that any other items like the pension are properly captured by those calculators.
It's also possible that your take-home pay will drop before April if your total YTD pay goes above an average of £4166/month (i.e. £50K/year) before then, as at that point your unused basic-rate band will be used up, so don't budget for it to continue until then unless you've done the calculations carefully.
Finally, although this answer assumes the standard numbers for the 2019-20 tax year of a tax-free allowance of £12,500 and hence a higher-rate tax threshold of £50,000, your tax code of 1151L as opposed to 1250L means the exact numbers are actually slightly different for you. But the difference in tax is in about the right ball park for it being unused basic-rate band, so that is probably the main or only explanation for the discrepancy.