Can add the new variable in the existing node--contenttype.tpl.tpl? I have written the query in .Module file and stored the output in a variable.

Now, I want to pass this new variable in existing node--contenttype.tpl.php

My idea is to pass the variable for the existing node.tpl.php using hook_theme function

Is that a good way to achieve it or anyone has a better way for it ?
You'd be better off doing in here:
https://api.drupal.org/api/drupal/modules%21node%21node.module/function/template_preprocess_node/7.x

"Processes variables for node.tpl.php" so should be ideal for what you need