The phrase "a traineeship with" is correct and usable in written English.
It can be used when referring to a training position or internship that someone is undertaking with a specific organization or company.
Example: "I am excited to apply for a traineeship with your esteemed company to gain valuable experience in the industry."
Alternatives: "an internship at" or "a training position with".
After reading English at Oxford, she took up a traineeship with the BBC.
After graduating with a 2 2, he started a traineeship with Planet 24, the company that produced The Big Breakfast and The Word.
Bergkamp has been on a traineeship with Ajax since July as he seeks to gain his coaching licence, working with both the first-team strikers and the youth team.
It is undeniable that many of the cleverest law students desire a traineeship with one of the Magic Circle, then a permanent job there, thence to their ultimate ambition - to become a partner.
By the end of his time at Cambridge, Frost had not only appeared in a television comedy sketch with Cook, but also had a traineeship with the London TV company Associated-Rediffusion, an agent and a cabaret gig at the Blue Angel club in Berkeley Square.
Thinking his hopes of a career in football were over, Rowan started a traineeship with a bank.
The immediate struggle for us wannabe solicitors is in obtaining a training contract – a two-year traineeship with a law firm.
Guardian Careers blogger and Legal Practice Course graduate Krishnan Nair explains: "The immediate struggle for us wannabe solicitors is in obtaining a training contract - a two-year traineeship with a law firm.
She then focused on finding an internship and through school's European and Eurasian Studies program, she landed at an international public affairs agency and soon after in a Bluebook Traineeship with the European Commission.
He won a scholarship to Oxford to read history, and in 1961 he gained a coveted traineeship with the BBC.
Gröning left school with high marks and began a traineeship as a bank clerk when he was 17, but war was declared shortly after he started employment and eight of the twenty clerks present were immediately conscripted into the army.
