The TEA will evaporate first, followed by water as you raise the temperature, and what is left over will be mostly AcOH. You can pull the rest of the water out of AcOH using molecular sieves or anhydrous magnesium sulphate.
You may need to turn you solution into basic by adding NaOH, most TEA will appear on the top as organic phase, separate the TEA, extract with ethyl ether for any leftover TEA.
Then acidify the aqueous phase with HCl, do distillation to recovery the AcOH.
But, both TEA and AcOH are cheap, why do you want to recovery them?
In my organic reaction, I used TEA in excess. So, washed aquous solution already in 8.5 pH. I added NaOH , But TEA is not recovered. If we recover TEA, organic load to the effluent will reduce.
Relative small amount of TEA will not show as second phase, it can be removed by rotor evaporation under reduced pressure, or extract with DCM(only in case your product does not dissolve in DCM).
Is your product inside the aqueous phase or the organic phase?
I recommended fractional distillation because it is impossible to gauge the pressure and bath temperature combination that would distill TEA but not water. If he wants to recover the TEA the best route is to use a rotovap-like setup, even using a dry ice finger would be acceptable, but either atmospheric or *slightly* less than ambient pressure, keeping the water bath at 89C constant. It will take a long time but it's the best way I know of to extract most of the mostly-pure TEA. You'll likely have some water condense along with TEA but a relatively small amount that can be dried in the same manner as usually, with sieves, silica, or anhydrous sulfate. The water can then be boiled off, again I would caution against using negative pressure as it is too difficult to anticipate how significantly you are impacting the vaporization pressure of the two remaining species. No azeotropes are formed between any of these, at least to my knowledge, so separating them should be straightforward if one is patient and willing. Cranking the temp up to 100C after most or all of the TEA has been removed will start to evaporate the remainder of water. This may take a while but I suggest you stick with ambient or only slightly below ambient pressure unless you know what you're doing (equipment, substances, volumes, ratios, heat, pressure, all of these variables can drastically effect heat of vaporization). The remaining liquid will be mostly pure Acetic Acid, which can be completely dried using any of the aforementioned methods and many more.
If you just want the TEA out and don't care about about the rest then you can just hook it up to a millibarr vacuum-coupled rotary evaporator with an ethanol-dry ice slurry finger/dry ice pick, and let loose. If you don't watch it like a hawk, however, your entire solution and whatever was in it will end up in the trap (if you cleaned the trap well beforehand then you can do it again, if not then you'll probably be starting the experiment over).