The IPG Mediabrands agency will work across UK-facing brands Unibet, Stan James, Bingo.com and Maria Casino. Nielsen figures show that the group spent £4.5m in the UK in 2016.
Initiative pitched against Havas Media and incumbent Goodstuff Communications.
Kindred reported profit before tax of £22.9m for the second quarter of the year, which includes the £2.6m acquisition of 32Red. In the same period last year, pre-tax profit was £15.4m.
Last year Unibet appointed Karmarama as its UK creative agency after a competitive pitch. The brand and Accenture-owned creative agency won the Grand Prix at the 2016 DMA Awards for "Luck is no coincidence".
James Temperley, head of broadcast at Initiative UK, said: "Like Initiative, [Kindred] boast a real people-focused business with a strong culture and a digital DNA, so we are confident that we will work extremely well together. They also have exceptionally strong brands in this very exciting and fast-paced field."