Yes, you can make a syrup out of anything.
Cloves provide a great flavor in Tiki drinks but they are powerful. You certainly can't use whole cloves in drinks and even ground cloves tend to not mix well. This leads to a much too strong clove flavor whenever you get a bit in your straw. It's not the kind of face you want folks to make after they sip one of your rum rhapsodies!
What you need is a solution solution. Like anything that doesn't mix well on its own, pre-mix with a bit of water and sugar. Then your flavored solution will provide the flavor you want in a mixable form that allows for much more control over flavor quantity.
Besides, it also makes a pretty mean glaze for hams.
As with all homemade syrups, I use swing-top stopper bottles for storage and quick pouring.
Clove Syrup
Source - Imbibe Magazine
1 cup unrefined sugar
1 cup of water
1/3 cup of cloves
In a small saucepan combine all the ingredients and bring close to a boil over medium heat. Stir constantly until almost boiling, then reduce heat to low and simmer for 20 minutes, stirring occasionally. Let cool at room temperature and strain into a clean bottle. Cover and keep refrigerated for up to 2 weeks.