I have a six-month UK visitor visa in my passport and the visa is going to expire on April 26, 2018. I have not used the visa to enter the UK yet and due to personal reasons, I will not be visiting the UK before the expiry of the visa. I plan to visit the UK in May 2018. Can I apply for an extension of the existing visa by 3 or 6 months?
My understanding is that you will need to apply for a new visa.
Extensions for long-term and multiple-entry visit visas (Link):
If a visitor holds a long-term multiple-entry visa and they want to stay for longer than the visa expiry date, it is possible for them to apply to extend their leave for up to the maximum 6 months permitted for visitors (standard). For example, a visitor arrives in January and their long-term visit visa is due to expire in February. Provided the visitor meets the rules, they can extend for up to 6 months, until June, as a visitor (standard). A single entry or 6 month visa can also be extended to complete 6 months’ in the UK as a visitor.
You will not qualify for the visa extension since on this page it states that you need to apply from inside the UK on the visa that needs extending (which you will not be).
You must apply while you’re still in the UK.