Hello Jane,
The linking issues drop-down is customizable, you just need to type gg in your keyboard when you are in your JIRA (To open the search bar) and type Issue Linking or navigate to JIRA Settings > Issues > Issue Linking.
You can add all kind of links you want on that page ('must be done before', 'must be done after', etc), however, I would like to let you know that this is not a "dependency" functionality itself.
Explaining better, the Issue Link feature is only to inform that this issue is linked to someone, however, it will not block the issue from being transitioned/Edited while the linked issues are not Done/Closed.
If you want to configure this kind of dependency on JIRA, you will need to use an Add-on. You can check the following post to know the suggestions we have to perform it and also vote and watch for the feature request below:
- Ability to prevent closing an issue if all linked "is blocked by" issues are not closed
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