You can add a web part zone under the quick launch bar. If you need that web part zone to be visible in all the pages you need to modify all the page layouts you have used for your pages, for example if you want to have a web part zone for a Blank Web Part Page Layout, open the website using the SharePoint Designer, goto _catalogs/masterpage folder. Open BlankWebPartPage.aspx search for the contentplaceholderid “PlaceHolderLeftActions”.
Add the following code in that content tags.
<WebPartPages:WebPartZone id="g_D9433DD058824E5E93304973959F6F0B" runat="server" title="Zone 1"><ZoneTemplate></ZoneTemplate></WebPartPages:WebPartZone>
Check In the page with the major version and make sure that the page layout is Approved.