Philippians 2:12-13 (English Standard Version)

Therefore, my beloved, as you have always obeyed, so now, not only as in my presence but much more in my absence,

work out your own salvation with fear and trembling,

13for it is God who works in you,

both to will and to work for his good pleasure.

From DA Carson's How Long O LORD? - the Mystery of Providence pg 210-211

This passage is extremely important, as much for what it does not say as for what it does. It does not say that God has done his bit in your salvation and now it is up to you. Still less does it suggest that because God is working in you "to will and to act according to his good purpose" you should therefore be entirely passive and simply let him take over. Nor is it( as not a few commentators wrongly suggest) that God has done the work of justification in you , and now you must continue with your own sanctification.

Paul describes what the Philippians must do as obeying what he has to say, and as working out (not working FOR!) their own salvation. The assumption is that choice and effort are required. The "working out" of their salvation includes honestly pursuing the same attitude as that of Christ (2:5), learning to do everything the gospel demands without complaining or arguing (2:14), and much more. But at the same time, they must learn that it is God himself who is at work in them "to will and to act according to his good purpose." God's sovereignty extends over both their willing and their actions.

Indeed, far from being embarrassed by this candid compatibilism, Paul sees in God's sovereignty an incentive to encourage the Philippians on their way. "Work out your own salvation" he tells them, " for it is God working IN you." God's sway in their lives is, for Paul, not a disincentive to action, but an incentive: get in step with what God is doing.