Nice to haves
Chelsea will likely need a new goalkeeper regardless as to what happens with the Kepa Arrizabalaga situation. The Blues do have the bodies who can fill in, but once the priorities are taken care of, then keeper can become one.
It seems unlikely that Arrizabalaga would leave this summer but it does not feel unlikely for him to have a challenger for the starting role. Andre Onana has been the most exciting name linked and he could certainly push Arrizabalaga.
A winger besides Sancho will come down to what Willian wants to do next season. If he wants to stick around, no one else will be needed. But if not, then the Blues could start looking around for an older winger to supplement the (potential) trio of Sancho, Pulisic, and Hudson-Odoi.
Wilfried Zaha is really the only winger that sort of fits that bill who has been rumored, but it is a low priority depending on what Willian wants to do.
Striker would be the last one and like with Sancho on the wing, a second signing for the same position would be more of an older or obvious backup. Olivier Giroud is sure to depart and Michy Batshuayi has little reason to stick around for meager minutes (again) so the Blues will need someone.
Moussa Dembele appears to be the front runner for the role, but whether or not he would join behind Abraham and (potentially) Werner is a mystery.