Triacylglycerols (TAGs) are basically fats - three fatty acids (FAs) linked to glycerol.
http://www-biol.paisley.ac.uk/course...lglycerol.html
I believe the proper name for "palmitoyl acid" is actually palmitic acid (PA). You can check chemfinder.com for the structure. It's a linear 16 carbon molecule with the carboxylic acid group on the end carbon.
To isolate PA from TAGs, you'd need a TAG with that FA substituted on the glycerol backbone. Then you'd need to sever the ester bonds connecting the FAs to the glycerol, and then you'd need to separate the PA from the other FAs and the glycerol.