Hello @Tetiana ,
Nice avatar!, so This are the steps to perform what you ask, as stated above, you will need to be a Jira admin in order to do this but I think it's good you understand what needs to be done.
I simulated your case in a project, as you can see I don't have the Story Issue Type set:
Go to your Project settings (need to be project admin for this):
In the left panel go to Issues -> Types
Here go to Actions -> Edit issue Types ( need to be Jira Admin for the next part)
Drag the Issues from Available to Current Scheme as per your requirements and then save it.
You will now see the Issue type on the Issue Type Scheme used by the project and on the issue search.
Hopes this clarify your questions, have an awesome day.
Welcome to the Atlassian Community!
The dropdown is listing the types available in the project. To add Story, you will need to add the Story issue type to the project's issue type scheme so the project can use it. To remove initiative, remove it from the project's sscheme.