What is a good antonym for "infest"? I thought of "cleanse" but I'm hoping there is a better antonym. The context I'm thinking of is when an exterminator gets rid of an insect infestation.
For animal pests you can see, exterminate is good. For microbes people generally use disinfect or sanitize.
"Purify" or "purge" come to mind as likely candidates.
There are many good ex- words besides exterminate (mentioned in an answer) and exterminator (mentioned in question), including: expunge, with sense "to eliminate completely; annihilate"; extirpate, with senses "to destroy completely; to annihilate" and "to pull up by the roots; uproot"; and excise, "to cut out; to remove". Other useful words include abolish, annihilate, eliminate, erase, obliterate, purge.
Eradicate is a suitable and fine-sounding word. Its senses include "to pull up by the roots; to uproot" and "to completely destroy; to put an end to; to extirpate".
As the verb 'infest' is used with the noun which is doing the infesting, I would say that a good antonym would describe the action of doing opposite of making yourself abundant in an area - making yourself scarce. Perhaps something like "evacuate"?
Good selection of words from the violent ('exterminate') to the poetic ('cleanse') and the clinical ('sanitize'). Infestation implies to me an out of control growth of some kind of pest, so you might want to use the image of wiping it out at its root - i.e. 'eradicate' it...