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Amir had been due to play for Kent in the second half of the Blast, after the completion of the PSL - but the shifting dates for the rearranged competition, which begins on Wednesday, and quarantine restrictions for arriving in the UK from Pakistan mean he won't be taking up his deal.
Instead, Milne will arrive for his fourth spell at Kent, having taken 38 wickets in 28 appearances between 2017 and 2019. He is expected to be available for Kent's ninth group game, against Somerset at Canterbury on June 28, onwards.
"We're delighted that Adam will be coming back to be a Kent Spitfire once more," Kent's director of cricket, Paul Downton, said. "He is a world-class T20 bowler who has made a significant difference to our side every time he has played for the Spitfires. I am sure our Members and supporters will be excited to welcome him back for the later stages of the Vitality Blast."
Milne was part of the Kent side that reached the quarter-finals of the Vitality Blast in 2018, and narrowly missed out on reaching the knockouts a year later. He has also featured at the IPL and the Big Bash, as well as being capped 23 times in T20Is by New Zealand.
Milne said: "I love being a Spitfire and I'm really excited that the opportunity has arisen for me to come back to Kent for a fourth time. It'll be great to see familiar faces in the dressing room but I'm also looking forward to working with the new talent that has joined since my last stint in 2019."
Kent's other overseas options include South African batter Heino Kuhn and the Afghanistan legspinner Qais Ahmed, who is expected to be available after quarantine from June 13, when the club face Gloucestershire at Canterbury.