You would want to do an in-gel tryptic digest on the gel plug. The process essentially decolorizes the gel plug first, then dehydrates it with acetonitrile. The trypsin solution is used to hydrate it. The peptides, being smaller, can leave the gel and go into the solution. That solution is then lyophilized. Here is my article describing the process and how we teach our students to identify the protein, in an educational journal. https://www.researchgate.net/publication/236049436_Seed_storage_proteins_as_a_system_for_teaching_protein_identification_by_mass_spectrometry_in_biochemistry_laboratory
The tryptic digestion procedure is mostly based on the method posted by Sigma-Aldrich