[5] Throughout Senior Bowl practices, Adams garnered attention and impressed scouts by showcasing his blocking ability and making multiple difficult catches.

[6] On January 30, 2016, Adams made three receptions for 49 yards and was a part of Jacksonville Jaguars head coach Gus Bradley's South team that defeated the North 27-16.

[7] Adams was one of 15 collegiate tight ends to attend the NFL Scouting Combine in Indianapolis, Indiana.

He ran the fastest 40-yard dash among all tight ends and finished seventh in the vertical jump and three-cone drill.

[10] At the conclusion of the pre-draft process, Adams was projected to be a third or fourth round pick by NFL draft experts and scouts.

He was the seventh tight end selected and was the last of three South Carolina players drafted, after Pharoh Cooper and Brandon Shell.

[16][17] Throughout training camp, he competed with Matt LaCosse, Larry Donnell, Will Tye, and Ryan Malleck for the job as the starting tight end.

Head coach Ben McAdoo named him the third tight end on the Giants' depth chart, behind veterans Donnell and Tye.

[18] On September 18, 2016, he made his professional regular season debut in the Giants' 16–13 victory over the New Orleans Saints in Week 2.

He made his first career reception on a 13-yard pass by Eli Manning in the fourth quarter before being tackled by linebacker Joe Thomas.

Adams entered training camp competing against Rhett Ellison, Tye, and LaCosse for the second tight end position behind rookie first round pick Evan Engram.