By default, email templates in Zoho CRM are module-specific. A template created for the Leads module is only available when you're working with a Lead record, and won't appear in the list when composing an email from a Contact, Deal, or any other module.
When creating a template, you choose the module it belongs to, and that choice determines where it's visible. If you want the same template usable from both Leads and Contacts, the two established options are to create it separately in both modules, or to clone the existing template into the second module rather than rebuilding it from scratch.
Zoho has begun rolling out a genuine fix for this: the ability to associate a single email template with more than one module, rather than needing separate copies. This rolled out to new sign-ups and Professional edition India data centre accounts first, then expanded to most other data centres.
If multi-module templates haven't reached your data centre yet, cloning is still the fastest workaround: open your existing Leads template, clone it, and change the clone's module to Contacts. This avoids rebuilding the content and merge fields from scratch.