Burns - a former chief executive of the Irish business of Aviva PLC - currently serves as non-executive at Hastings Group Holdings PLC. She will join the firm from the start of April. On appointment, she will become a member of the audit, nomination, remuneration and risk committees.
"We are delighted to welcome Alison to the board," Equiniti Chairman Philip Yea said. "Her financial services and insurance background will provide an invaluable resource to support Equiniti's strategy over the coming years."
Jarman - a non-executive since 2014 - will step down from Equiniti at the annual general meeting in May.
"I would like to place on record the board's thanks to Vicky for her valuable contribution and commitment to the board and the company during her four year tenure," Yea added. "The board has benefited greatly from her experience and advice."
Shares in Equiniti were 1.9% higher at
