How to outrank an old URL

About all you can do is to keep doing SEO to try and outrank the old website. If it was popular, well established and high in the rankings it could take awhile.

A perfectly ethical but sneaky trick: Check https://lookup.icann.org/ to see when the old domain name expires.

Keep an eye on it. The old owner may have no interest in renewing a domain name when it expires. You could pick up the old domain name and redirect it to your new website or rebuild it.

Step 1: Audit Your Content
The process all begins with auditing and evaluating your content.
There are basically three buckets of content:
Content that helps you.
Content that does absolutely nothing for you.
Content that can hurt you.
We need to figure out which bucket all of our content fits in.

Step 2: Evaluate the Quality of Your Content
Next, you'll need to analyze the quality of the content you have on the website.
Step 3: Determine What to Do with Your Existing Content
The final step of this process is making data-driven decisions about whether you should improve (update, rewrite, or consolidate) or remove (deindex) old content from search engines.

Thanks, I am also learning these things because I have goal to start my own blog one day.

If I am in your shoe, I would try these...

First, make sure the new site is up and running, with at least 10 quality content published. These contents should also target relevant keywords as the content on the old blog.

Then I will run a backlink analysis for the old domain with a link analysis tool.

I will gather in spreadsheet all external links pointing to the old domain, then I will reach out to the owners of every website in this spreadsheet to consider editing the link on their website to point to the new domain. Since the old blog no longer exists, I think this strategy will work.

If things worked out as expected, you should see the new domain outrank the old in not too far distance. Though it will take some time, this should work.

If the page is dead then also inform Google and explain that your new URL is the correct one. This is as well as what everyone else here has said also.

Hey Folks, I have the same issue:
Introduction : We have two products which are very similar in nature and both of them have seperate web pages. One of our product is already live in the market and has really good search engine rankings while the other product is about to be launched soon.

Our concern: With the launch of this new product, we might not be able to make this product rank in the first page of Google as Google does not promote two similar pages from the same domain to rank of first page. Also, the keywords for the both the products are going to be similar/same in many cases which I am concerned will affect our existing product's ranking once the new product goes live.

Example: To help you imagine the nature of products you can think that our business is of food delivery. Until now we have been an an aggregator which aggregates food from various restaurants and delivers it. We have a current webpage which ranks on the first page of google. Now we are going to launch our own cloud kitchen for which we will have a separate web page.

Challenge : How do we make this new web page rank high on Google with the limitation that the popular keywords like order food online, order food etc are already optimised for our existing business and we don't want to impact this.

One probable solution : Make webpage of the new product as the parent page and the webpage of existing product as child page. And then re-distribute keywords between these two products. More intent specific keywords towards new product page(parent page) and less intent specific keywords towards existing product(child page).

Can someone please tell me how can we solve this problem where we can make sure that Google treats these two pages differently and both our pages have good chances of ranking on the first page?