The LA Clippers did add Brook Lopez this summer, who started 466 out of 469 games for the Milwaukee Bucks, but he was not brought in to compete for Ivica Zubac's role. In fact, the Clippers added him because of his previous experience with Zubac, and they believe he would be the best backup center in the NBA.
Thus, the keys for the starting position belong to Zubac and will remain in his keychain throughout the foreseeable future. This locks in a third of the frontcourt, with another third going to Kawhi Leonard, who has also started 264 out of 266 games as a Clipper.