In our study of any portion of Scripture, we should first of all look at the address on the envelope. Of course, you would say that the recipients were in the city of Philippi. That is true, but there is more to it than merely their earthly residence. They are a people whose citizenship is in Heaven (Phil. 3:20). That immediately sets them apart. They are not of the dispensation of promise, for all connected with it have a part in the promise made to Abraham, and that had to do with a specific land on this earth as we know it, heaven not being their hope.
Up till the end of Acts, Paul was preaching The Kingdom, and he expected to be living when The King came to take up His Kingdom (1 Thes. 4:15 & 1 Cor. 15:51). But in Phil. 1:23 Paul has the desire to depart, that is, a return to the dust to sleep in Christ until Manifesting with Christ Jesus in The Heaven of heavens. The Kingdom is no longer in view, so he is resigned to the fact that he must die someday.
From the beginning of his ministry till the end of Acts, Paul had spiritual gifts, one of them being the gift of healing (Acts 28:3-6; Acts 28:8-9). But we know that Philippians is written after the time of Acts 28:28 from history but mainly because of the account of the sickness of Epaphraditus (Phil. 2:25-30). Paul could no longer heal the sick, and there is no recorded sign, miracle, or wonder after the event of Acts 28:28.
However, you may understand it or read it: the high calling of Phil. 3:14 cannot possibly have to do with the dispensation of promise and its Kingdom. This is something over and beyond a Kingdom here on earth.
Paul spent the early years of his ministry in a dispensation in which the Jew was first. At that time, Paul had much about which he could boast (Phil. 3:4-6). But with the change of dispensation, Paul no longer had whereof he could boast. He counts all such things as loss in The Dispensation of The Mystery.
Now, with the address problem settled, we find that we are to work out our salvation with fear and trembling (Phil 2:12). Notice that it says work out, not work for. Our Salvation is by Grace through Faith (Eph. 2:8-10). Also, we can see that it is not the salvation which was of the Jews (John 4:22), but the Salvation that was sent to the Gentiles (Acts 28:28). In his first seven epistles, Paul wrote of the salvation which was of the Jews for at that time they had every advantage, including the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises (Rom. 9:3-5). He went to the Jews first and then to the Gentiles, for at that time, the Gentile believer partook of the blessings of Israel. So, we can conclude that The Salvation that we are to work out today is that which was sent to Gentiles.
You might find another title for this Book in Phil 3:14, The Prize of the High Calling (we would like to offer you a book on that subject for free). We do not know what this prize might be, for it is not described. Overcomers in the Kingdom of Promise calling will rule over the nations with Christ (Rev. 2:26-27), and that here on the earth. There is a hint in 2 Tim. 2:11-12 that there may be a similar situation in The Dispensation of The Mystery, that there may be a ruling in Heaven with Him.
Although Philippians and Hebrews are in two different dispensations, they have a common theme: On to Perfection.
