Enhance photo output on card stock

The Canon TS3522 printer is a very basic printer with just one cartridge for color and one for black.  I don't think it is capable of printing "postcard" photo quality even with glossy or matte paper.  So I don't think I would waste a lot of ink trying to get a better result than you are currently getting.

Sharpen.   When you sharpen an image it focuses on edges for the most part.

When I want stuff like postcards:  I send it off to a printing service--- it's like home printed business cards-  they simply are not very impressive- and quite often the ones I see pinned up in grocery stores tend to look very amaturish.

A few AI words about glossy paper:

Glossy paper gets its shine from a smooth, reflective coating applied during manufacturing. This coating, often made of materials like kaolin clay, calcium carbonate, or polymer resins, fills in the paper's natural texture, creating a sealed and smooth surface. This prevents ink from soaking in deeply, enhancing color brilliance and image sharpness. 

As Bill says, the key issues are the printer settings and the paper and whether they are made for each other.  The printer has different profiles that it uses for different papers.  

Another variable is whether the profile that is being used for the printer is managed by the printer or Elements.  You can find this setting under the More Options dialog found in the Print dialog. 

In that dialog, you will also see various color profiles that are available depending on which option you choose for managing the color.  This is a very complex issue and entire books are written about it.  So you are going to have to do some trial and error to see what works best for you.

BTW, is the postcard stock actually for photo printing?  And what printer do you have?

The key variables include the printer and the paper and will be different for each system.   If it were me, I would try adjusting exposure, contrast and saturation until I liked what I see.