So...you want to draft a TE in the 1st round.
Here's a little history lesson from the internet
Seems like the only real way you end up with a really good tight end is taking mid-round guys at good value and hope that they develop.
If you look at the TE's you'd want to have on your team the names are:
Kelce (3rd), Kittle (5th), Waller (6th), Andrews (3rd), Goedert (2nd), Schultz (4th), Freiermuth (2nd), Gesicki (2nd).
Teams who spend first round picks on tight ends, those guys rarely get 2nd contracts from that team: Hockenson, Fant, and Hurst were all traded before they became free agents. The Bucs didn't bother extending O.J. Howard after picking up his 5th year option, Eric Ebron got released by the Lions (but played better for other teams), Tyler Eifert signed two one year "prove it" extensions with the Bengals then left, Jermaine Gresham played out his rookie contract with the Bengals then left, etc.
To find a first round tight end that actually got signed to a real extension by the team that drafted him you have to go back to 2009 with Brandon Pettigrew, who wasn't exactly setting the world on fire. That was 14 years ago"