Please add the following DNS records at Namecheap control panel:

Type: MX

Name: @

Mail server: mx1.hostinger.com

TTL: auto

Priority: 5

Type: MX

Name: @

Mail server: mx2.hostinger.com

TTL: auto

Priority: 10

Furthermore, to help with outgoing email deliverability, you will also need to add the following SPF and DKIM records:

Type: TXT

Name: @

Value: v=spf1 include:_spf.mail.hostinger.com ~all

TTL: Default value

Type: CNAME

Name: hostingermail-a._domainkey

Target: hostingermail-a.dkim.mail.hostinger.com

TTL: 300 seconds

Type: CNAME

Name: hostingermail-b._domainkey

Target: hostingermail-b.dkim.mail.hostinger.com

TTL: 300 seconds

Type: CNAME

Name: hostingermail-c._domainkey

Target: hostingermail-c.dkim.mail.hostinger.com

TTL: 300 seconds