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You are always liable to Capital Gains Tax (CGT) on the gain between the eventual sale price less costs of sale and the probate value; not many people realise this. However, as it was your sole or main domestic residence you are entitled to Private Residence Relief (PRR). PRR reduces the gain by 100% to nil so on sale there are no CGT implications. The time delay is an irrelevance.
I do hope I have been able to bring you some good news.
There are no tax implications pursuant to the delay. Your Mother's estate will have met any Inheritance Tax (IT) due, but her estate would have to have exceeded 325K plus any charitable bequests plus any unused IT exempt portion from her original spouse's estate for IT to kick in anyway.
The delay factor does not matter; effectively you and your sister entered into a Deed of Family Arrangement to amend the provisions of your mother's will.
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