Only if you need to open the prior year .tax file or if you need to amend a prior year. You can always reinstall the program. But they only support the last 3 years (currently back to 2016).
But first I would open each year in the program and save it as a PDF file, go to File-Save to PDF so you don't need the program installed to view or print your return in the future like to get a mortgage or loan, etc.
You should save all the .tax files and pdf files to a flash drive or burn to a CD or DVD or copy them to an external backup program for backup.
I'm a little confused by your question because you asked about "TurboTax app on the computer," but when you posted the question you selected TurboTax Online as the product you are using. (See the gray oval at the bottom of your question.) If you used TurboTax Online in previous years, there is nothing on your computer to keep.
If, however, you actually used the CD or download TurboTax software installed on your computer, I would keep at least the most recent previous year so you can refer to it while you are working on this year's tax return. If you don't need the space on your hard drive, keep the most recent three previous years in case of any IRS inquiries, or in case you discover a need to amend.
The new tax bill that the president just signed last week retroactively reinstates for 2018 and 2019 some provisions that had expired at the end of 2017. If any of the reinstated provisions would be of benefit to you, it might give you a reason to amend your 2018 tax return.