There are couples of plugins of WordPress, such as Easy WP SMTP, for sending emails but you have to setup the right SMTP server. Here is the way about using Hostinger SMTP.

When you search on internet, the SMTP server of Hostinger is usually shown as:

• Protocol: Outgoing server (SMTP)
• Hostname: smtp.hostinger.com
• Port: 587

It might not be correct. another way to check the SMTP is to access Email > domain name > Set Up Devices > Manual Configuration

direct link: https://hpanel.hostinger.com/email/[domain name]/setup-devices

In my panel, anything is the same but the port is 465.

Unfortunately, it might not be correct as well. the only correct information is to check out Hosting > domain name > Details > E-mail details

direct link: https://hpanel.hostinger.com/hosting/[domain name]/accounts/details

In my panel, it is shown as:

• Protocol: Outgoing server (SMTP)
• Hostname: smtp.hostinger.com.hk
• Port: 587

This is the correct one and now you can setup the configuration.

• From Email Address — the email address you use to send email and to be accessible by SMTP
• From Name — the name of the sender.
• SMTP Host and Port — the SMTP details you obtained as mentioned.
• Type of Encryption — select TLS protocol
• SMTP Authentication — select the Yes option.
• SMTP Username and Password — the login details of your mail address chosen as sender.

There is a test email section for Easy WP SMTP and you will see the result.