I've a requirement to show some custom links in OOTB "community tools" webpart (which will be shown only to community owners and moderators).
I've to remove few links and add some custom links to that web part, How can I do that?
The community tools web part, is part of the site template and not intendet to be edited. These links have been selected by the development team of the community feature to make management simpler.
Editing the web part isn't supported. One option to overcome the problem is to delete the Community Tools Web Part and customise a Content Editor web part making it look like a Community Tools Web Part. Links to add can be found from the CT Web Part.
You have two options:
If you only want the web part to be visible to users in the community's owners and moderators groups (as you mentioned in your comment beneath your post), you can enter these group names into the "Audiences" property in the web part properties tool pane.
Pros: Your imagination is the only limiting factor here as far as customization goes.