The energy to attach a third phosphate to ADP (to make ATP) ultimately comes from the breakdown of food molecules during cellular respiration, mainly from glucose and other nutrients.

Immediate energy source

Inside cells, ADP is converted to ATP in two main ways, and in both cases the needed energy is first extracted from nutrients.

• In substrate‑level phosphorylation, a high‑energy phosphate group is transferred directly from a phosphorylated intermediate (a “high‑energy” metabolic intermediate) to ADP; the energy in that intermediate’s bond is what drives formation of ATP.

• In oxidative phosphorylation, energy from electrons taken from nutrients (via NADH and FADH₂) is used to build a proton gradient across the inner mitochondrial membrane, and the flow of protons back through ATP synthase provides the energy to add the third phosphate to ADP.

Big picture source

The high‑energy intermediates and reduced carriers (NADH, FADH₂) that power these processes are generated when cells oxidize carbohydrates, fats, and sometimes proteins.

So, in summary, the immediate energy comes from high‑energy phosphate compounds and the proton gradient, but the original source is the chemical energy stored in the food molecules the organism has metabolized.