Teammates do not automatically have access to each other's contracts; this is intentional, both to avoid needlessly cluttering people's contract inboxes with deals that aren't relevant to them, and for purposes of safe data handling.
Contracts contain information for specific deals, and therefore should only be shared with people to whom they are relevant: those who are participating directly in the process for that deal, those in an oversight/supervisory role, or those requiring access due to some regulatory mandate.
Never Fear, Auto-Share Is Here!
That said, it's easy to enable a template-level feature that automatically shares contracts with specific users! With a template open, click Settings (gear icon). Then, add teammates from the list who should be automatically shared on contracts generated from this template:
Don't forget to set appropriate permissions for auto-shared users:
For more detailed instructions on this feature, click here.