The verses deal with how Christians can be sure of their calling and election into the kingdom of Jesus Christ. Diligence needs to be applied to certain things to prevent their faith in being so called and elected weakening. If their assurance about this weakens, they will begin to stumble. They won't be prevented from entering the kingdom, for they have been called and are elected to be in the kingdom, and other N.T. texts show that they have already found entrance in.
That is confirmed by what Jesus said in answer to the question, "Lord, are there few that be saved?" He had just given several parables about what the kingdom of God was like. His answer was:
"Strive to enter in at the strait gate: for many, I say unto you, will
seek to enter in, and shall not be able." Luke 13:23-24 A.V.
Jesus said he is that gate which opens up to the narrow way (John 10:7-9). Those who do not enter into the kingdom via him remain on the broad way that leads to destruction for many (Matthew 7:13-14).
Going back to the text in question, Peter is addressing Christians who have already entered in via the strait gate (Christ) and who are now on that narrow road. His salutation is to those who have received faith in righteousness of God and Christ. Peter immediately launches into how to avoid being barren or unfruitful in the knowledge of Christ. But those who lack things like virtue, knowledge, self-control and love are blind and have forgotten that they were purged from their old sins. Now comes verses 10 and 11.
Christians can be sure of their calling and election into the kingdom of Jesus Christ. How? Diligence needs to be applied to certain things to prevent their faith in being so called and elected weakening. If their assurance about this weakens, they will begin to stumble.
On the contrary, Peter says that if they are diligent about exercising faith, virtue, knowledge, self-control and love, they shall never fall. That will keep them assured that when they have finished their earthly course, they will (without question) be ushered into heaven, where Christ is the King of the kingdom.
The answer to the question, "Does this passage imply that our entering into the kingdom is somehow contingent upon us growing in the qualities listed earlier in the chapter?" is no, not "contingent" to entering into the kingdom, but necessary to prevent believers stumbling or falling along the narrow way they are already on. Paul says something very similar in Colossians 1:10-14 where the Christians will be strengthened as they walk in the knowledge of Christ, being fruitful, having patience, long-suffering, thankfulness and joy, because they have been delivered from the power of darkness and have been translated into the kingdom of God's dear Son. Not, "Will yet be translated"!
"What is the entrance into the kingdom of heaven?" Having entered in to the kingdom via faith in Christ, they enter into heaven itself at the end of that journey on Earth along the narrow way, ideally without having stumbled or fallen en route to heaven!