"To complete an internship" means to finish or successfully end a period of work experience or training in a specific field or company. Full definition
After completing my internship at a not for profit agency, I was hired serving 12 years and then went on to serve as Clinical Director for another 4 years. (psychologytoday.com)
They have completed an internship in small animal medicine and surgery followed by a two year or three year residency program. (vrcc.com)
She left the business earlier this year after completing her internship. (vets-now.com)