Remove the water with a Dean-Stark trap to shift the equilibrium to the ester

The reaction with SOCl2 and anhydrous methanol in the presence of proline will give quantitative esterification after stirring +12h at RT and removing solvents. Likely equivalent to anhydrous HCl gas and methanol.

Proline (or Pyrrolidine-2-carboxylic acid) has -NH- in the 5-membered ring, so the use of HCl as a catalyst must be avoided because an ammonium salt will be formed.

If you can skip Fischer esterification, then I have this suggestion:

First reflux proline with thionyl chloride(SOCl2) for less than half an hour (20 minutes worked with an experiment I did on glutaric acid which is a dicarboxylic acid). The -COOH will become -COCl ( a highly reactive group).

Carefully mix the resulting compound with dry methanol & apply very mild reflux in the hood. Place a wet blue litmus paper on the top of the condenser. If it turns red, then HCl is leaving the reaction flask through the condenser. If NOT, then add cautiously but fast little pyridine or triethylamine (as HCl scavenger). The time of reaction starts from 2 hours & my advice is try 2 or 3 different times to optimize the yield.

Thanks a lot, I will try these conditions.