Rod Woodson played the most seasons with 3+ interceptions, with 14 seasons.

who has the most 3 interception seasons in a career
Interpreted as:
Who has the most 3 or more defensive interception seasons in a career?
WoodsonGreenBrownRileyLeBeauReedRobinsonLottKrauseFischerTunnellSharperWoodsonBuckleySandersAllenWallsShellBlountBarneyBrownAdderleyWilson1412121212111111111111101010101010101010101010
NAMEGPSEASINTTKLASTCOMBSCKSCKYINT YDSINT TDFFFRFR TD
Rod WoodsonRod Woodson21914681263215813.51,420111291
Darrell GreenDarrell Green18512440.0504562
Dave BrownDave Brown18412590.0693590
Ken RileyKen Riley16612600.05805140
Dick LeBeauDick LeBeau1651262762371
Ed ReedEd Reed16411635011086096.0561,567711132
Eugene RobinsonEugene Robinson17011514.06571161
Ronnie LottRonnie Lott15211607.56354150
Paul KrausePaul Krause15511731,0863173
Pat FischerPat Fischer14911498464111
Emlen TunnellEmlen Tunnell13011761,2544160
Darren SharperDarren Sharper15110604461275737.51,3309841
Charles WoodsonCharles Woodson156105648111359410.0798911131
Terrell BuckleyTerrell Buckley1571045564602.068751111
Deion SandersDeion Sanders13410457181.01,15680100
Eric AllenEric Allen15310483.0719860
Everson WallsEverson Walls14710551.0504140
Donnie ShellDonnie Shell14610471.04071151
Mel BlountMel Blount15010510.0640192
Lem BarneyLem Barney12610541,0156160
Willie BrownWillie Brown1321045394140
Herb AdderleyHerb Adderley13710471,0377130
Larry WilsonLarry Wilson1301046722491
Night Train LaneNight Train Lane12310631,149581
DeAngelo HallDeAngelo Hall1399415371476841.57.578848134
StatMuse has season-level data for interceptions going back to the 1940 season.