Maybe go after a blocking TE, but other than that, I wouldn't spend big money on the position. If you've noticed, Mitch Trubisky has had more success without the TE position being emphasized. A lot of 4-wide the last 2 weeks, especially in Detroit.
But I think the team will treat this season as a wash for Burton. He was hurt. And the contract says they'll give him another chance. With Horstead developing, I don't think they necessarily need another undersized pass catching type. I'd also bring back Holtz and Dax Raymond. Also, there's no reason not to at least bring Shaheen back for training camp. Other than that, I'd draft a TE. I'd love Brycen Hopkins with one of the 2nds. If not, definitely in the 4th or with a trade down to the 3rd.
Go into camp with a depth chart of:
U- Burton, Horstead, Raymond
Y- Holtz, cheap FA (takes place of Sowell), Shaheen
Drafted TE would likely be someone that could potentially learn both roles. Not a lot of good blockers in this class, but some good size.