Hi Hardik,
Looking at the above image, I suspect this is quite an old CRM onpremise version. However, there are a few things you need to check for the issue you have mentioned.
1. Check if there is any 1:N relationship on Territory entity with the custom entity you want to show the "add existing" button on the subgrid.
2. Check if the subgrid property is defined as "Only Related records".
For eg: I have an Accounts subgrid on my Territory form and this is how I have defined the properties.
This is how it looks on the form.
If the above settings are in place but still not working, then check if there are any ribbon customization made on the subgrid for the effected entities.
Thank you!
