Allison+Partners' role covered the US and UK. Bite is understood to have the same remit.
Neither Next 15-owned Bite nor ARM would comment on the appointment. Bite is reporting to Austin, Texas-based senior director of public relations Phil Hughes.
MDC-owned Allison+Partners had worked for ARM for just one year. Before that it worked with Racepoint Global for a number of years. ARM's UK-based senior PR manager Alexandra Harrod was a client director at Racepoint until the end of 2015.
"Our contract with ARM ended in May of this year," said Jonathan Heit, Allison+Partners' global president. "We accomplished a wide range of objectives together and are excited to see what’s next for the brand."
ARM was bought by Japan's SoftBank in 2016 for £24.3bn ($32.6bn), with Finsbury advising the acquiring firm around the deal.