The word beginning verse 7, "casting" is an adverbial participle. It is not the main verb. Verse 7 is a dependent clause, i.e. it's meaning is dependent upon the main clause, found in verse 6.
This is the complete thought broken down phrase by phrase:
6 Humble yourselves, thereforeThe main verb is "humble." It's an imperative, a command. "Casting all your anxieties on him" modifies the main idea, and "because he cares for you" modifies the action of casting our anxieties. The meaning of verse 7 is fuller by taking into consideration the main idea of the entire sentence.
under the mighty hand of God
so that at the proper time
he may exalt you,
7 casting all your anxieties on him
because he cares for you.
Taking into consideration the background and purpose of the book gives the sentence even more significance. The recipients of I Peter were enduring trials (1:6; 4:12-19) and Peter's purpose in writing is to instruct them with regard to handling themselves in this environment. By the time he gets to 5:6-7, he has discussed how to suffer well. As he reaches the conclusion of his letter, his command to humble themselves is timely. Part of the attitude toward suffering is humility.
The word, "humble" in 5:6 means to make low. The verb is a passive imperative, an action which Peter is asking them to do to themselves. Another way to translate this is "be humbled." The idea here is that we are to be fully dependent upon the Lord, to recognize that he is greater than we are. Think about a dog, going to her master when she's found digging in the yard or shredding the bathroom garbage (I have much experience with both of these phenomena). She will shrink low, put her ears back, and her tail between her legs. She knows she is confronting a power higher than herself.
When we consider the two phrases "humble yourselves" and "casting all your anxieties on him," we have a complete picture. Humbling ourselves is a first step in casting our cares on God. If we don't humbles ourselves, it may be too easy to simply cast them on our own devices. We are not always aware when we struggle to release control, but we all do it.
I Peter 5:7 is often used to try to comfort those who struggle with anxiety, and it is often said without the first part of the verse, humbling ourselves. Many who struggle with anxiety fear a loss of control. That makes it hard to humbles ourselves, because at its core, humility accepts a lack of control. When we struggle to release control, we may struggle to cast our anxieties on the Lord, whether it is because we are suffering or because we are simply anxious about something. When we are anxious, we may feel weak and burdened, but that doesn't mean we aren't still trying to gain control in order to ease our anxiety. Our first step needs to be to humble ourselves. Of course, it's not a magic cure, and every situation of anxiety is unique, but for the day to day anxieties we face, it's a good place to start.
I haven't got it all figured out yet, and I suspect no one else does, either. Trials are a part of life in Christ. And humbling ourselves under the mighty hand of God is the only way we can make sense of them. Notice what Peter says at the end of verse 6: "so that he may exalt you." We are only exalted when we allow Christ to work in us. That means that we need to be made low and let him reign. We have to relinquish the reins of control. This is a lesson I must learn daily.
See what we learn when we take the whole sentence in consideration!