Pace doesn't like to have to depend on the draft for starters. He seems to try to fill a hole in free agency, although it may not be with a top notch guy (i.e. Glennon, Mike Davis).
Will Demetrius Harris be the only FA TE signed? If so, then it looks like TE in round 2.
The only other factor is whether Burton is totally healed. He wasn't last year but when he was, he was effective in 2018. May help reduce the cap $ devoted to the TE spot.