Luke Wright has been and gone, to good effect, while James Fuller is also in the 12 for today.
Nash spent time at the Cornwall club several years ago, had a T20 strike rate of 125, and average of 27 in the last English season.
"We're sure he'll add value around the dressing room and will bring a bit of leadership, too," Auckland Cricket boss Mark Cameron said.
Auckland have lost four players to the New Zealand ODI side, opener Martin Guptill, middle order hitter Colin Munro and bowlers Kyle Mills and Mitchell McClenaghan, which will test the depth.
They have won two and lost one of their three games but will relish tackling the defending champions Otago, who welcome back test opener Hamish Rutherford.
Leaders Northern Districts are also unveiling a new import today, New South Welshman Chris Tremain, for their game against bottom side Central Districts at Nelson.
The tall, fast-medium bowler from Dubbo has been released from the Sydney Thunder until later in the Big Bash League. Tremain has taken 18 first-class wickets for New South Wales and played five T20 games for the Thunder.
ND are without Dan Vettori, who is at the BBL with the Brisbane Heat but have former international Scott Styris back after a calf injury.
Allrounder Anton Devcich plays his first game this season after his limited-overs time with New Zealand in Bangladesh and Sri Lanka.
Test wicketkeeper BJ Watling bolsters ND too, as they look to protect their lead.
In the third game today, Wellington host Canterbury at the Basin Reserve.