List all permissions for all table types.

SELECT 
  [schema] = s.name, 
  [type] = t.name, 
  [user] = u.name, 
  p.permission_name, 
  p.state_desc
FROM sys.database_permissions AS p
INNER JOIN sys.database_principals AS u
  ON p.grantee_principal_id = u.principal_id
INNER JOIN sys.types AS t
  ON p.major_id = t.user_type_id--.[object_id]
INNER JOIN sys.schemas AS s
  ON t.[schema_id] = s.[schema_id]
WHERE p.class = 6; -- TYPE

Grant EXEC permission on Data Type

GRANT REFERENCES, EXECUTE ON TYPE::dbo.MyDateType TO MyRole;