Yes, but what you can do will depend on the email account.
Go to Settings->Passwords & Accounts->"account name".
From there, you may see an option for "Mail Days to Sync" that will determine how far back emails are kept. If you set to 3 days for instance, you will only have 3 days worth of emails for that account on your iPhone at any time.
Again, the option depends on the email account, some providers may not show that particular option, and if the email account is a POP3 account, it just downloads everything, so the only way to keep the emails down is to actually delete them for those types of accounts.