No. Once you've closed your PayPal account, it cannot be reopened. You can open a new account, but it won't include your previous transaction history.
Here's a video to show you how to create a new Personal account:
Can I reopen a closed dispute in my PayPal account?
Can I add a foreign bank account to my PayPal account?
Can I view a monthly statement of my PayPal account?
Which cards can I use with my PayPal account?
Can I withdraw funds from my PayPal account to my credit card?
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