When I shift to the highest gear on my bike it is still too easy to pedal. Can I add gears to make it harder?

You can't easily add gears but you can change your gears. You have a choice of getting a smaller rear cog or a larger front chain-ring, or both. You may need a longer chain if you use a larger chain-ring.

Some answers here are missing a point.

You can do what you want with your money. Your results may be less than expected, though. If you do go with larger front chain rings expect to change your chain too. The entire drive train is made to work together. Changing one part of it effects the rest.

Your best bet is to spin what you have, or perhaps a new bike is in order.

You cant add any more gears than you already have but you can make them higher. You can either change the front chain ring by getting one with more teeth or can change the cogs on your rear wheel by getting one with less teeth. Either action will give you a higher gear. Changing the cogs on the back is easier. The smallest cog you can get is an 11 tooth. If you change the front chain ring to a bigger one you can go really big but any radical changes may require new derailers or at least moving the front one to accommodate the larger chain ring. Best to consult your local bike shop.

change your big front plate, look for one with more teeth, for mtb you can go for a 44 or 48 teeth plate instead of the common 42

It would help if we knew what you are riding now.

What kind of bike are you riding? How many teeth does your largest front sprocket, or chainwheel, have? How many teeth does the smallest cog on your rear wheel have? How fast is your pedal cadence?

No, (generally) you can't add gears. But you may be able to change the relative sizes for a higher gear ratio.